Journal of Approximation Theory最新文献

英文中文

Localization for random CMV matrices 随机 CMV 矩阵的定位

IF 0.9 3区数学 Q2 Mathematics

Journal of Approximation Theory

Pub Date : 2024-01-05 DOI: 10.1016/j.jat.2023.106008

Xiaowen Zhu

We prove Anderson localization (AL) and dynamical localization in expectation (EDL, also known as strong dynamical localization) for random CMV matrices for arbitrary distribution of i.i.d. Verblunsky coefficients.

我们证明了任意 i.i.d. Verblunsky 系数分布的随机 CMV 矩阵的安德森定位（AL）和期望动态定位（EDL，又称强动态定位）。

引用次数: 0

Comonotone approximation of periodic functions 周期函数的 Comonotone 近似值

IF 0.9 3区数学 Q2 Mathematics

Journal of Approximation Theory

Pub Date : 2024-01-05 DOI: 10.1016/j.jat.2024.106015

D. Leviatan , M.V. Shchehlov , I.O. Shevchuk

Let $\tilde{C}$ be the space of continuous $2 π$ -periodic functions $f$ , endowed with the uniform norm $‖ f ‖ ≔ {max}_{x \in R} | f (x) |$ , and denote by $ω_{m} (f, t)$ , the $m$ th modulus of smoothness of $f$ . Denote by ${\tilde{C}}^{r}$ , the subspace of $r$ times continuously differentiable functions $f \in \tilde{C}$ , and let $T_{n}$ , be the set of trigonometric polynomials $T_{n}$ of degree $< n$ . If $f \in {\tilde{C}}^{r}$ , has $2 s$ , $s \geq 1$ , extremal points in $(- π, π]$ , denote by $E_{n}^{(1)} (f) ≔ inf_{T_{n} \in T_{n} : f^{'} T_{n}^{'} \geq 0} ‖ f - T_{n} ‖,$ the error of its best comonotone approximation. We prove, that if $f \in {\tilde{C}}^{r}$ , then for either $m = 1$ , or $m = 2<设 C˜为连续 2π 周期函数 f 的空间，赋有均匀规范‖f‖≔maxx∈R|f(x)|，并用ωm(f,t) 表示 f 的第 m 次平滑模。用 C˜r 表示 r 次连续可微分函数 f∈C˜ 的子空间，设 Tn 是阶数为 <n 的三角多项式 Tn 的集合。若 f∈C˜, 在（-π,π] 中有 2s, s≥1 个极值点，则用 En(1)(f)≔infTn∈Tn:f′(x)Tn′(x)≥0,a.e. in(-π,π)‖f-Tn‖ 表示其最佳 comonotone 近似的误差。我们证明，如果 f∈C˜r，那么对于 m=1，或 m=2 和 r=2s，或 m∈N 和 r>2s，En(1)(f)≤c(m,r,s)nrωm(f(r),1/n),n≥1，其中常数 c(m,r,s) 仅取决于 m、r 和 s。求助PDF {"title":"Comonotone approximation of periodic functions","authors":"D. Leviatan , M.V. Shchehlov , I.O. Shevchuk","doi":"10.1016/j.jat.2024.106015","DOIUrl":"10.1016/j.jat.2024.106015","url":null,"abstract":"<div>Let <math><mover><mrow><mi>C</mi></mrow><mrow><mo>˜</mo></mrow></mover></math> be the space of continuous <math><mrow><mn>2</mn><mi>π</mi></mrow></math>-periodic functions <math><mi>f</mi></math>, endowed with the uniform norm <math><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo><mo>≔</mo><msub><mrow><mo>max</mo></mrow><mrow><mi>x</mi><mo>∈</mo><mi>R</mi></mrow></msub><mrow><mo>|</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>|</mo></mrow></mrow></math>, and denote by <math><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi>m</mi></mrow></msub><mrow><mo>(</mo><mi>f</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math>, the <math><mi>m</mi></math>th modulus of smoothness of <math><mi>f</mi></math>. Denote by <math><msup><mrow><mover><mrow><mi>C</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>r</mi></mrow></msup></math>, the subspace of <math><mi>r</mi></math> times continuously differentiable functions <math><mrow><mi>f</mi><mo>∈</mo><mover><mrow><mi>C</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow></math>, and let <math><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub></math>, be the set of trigonometric polynomials <math><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub></math> of degree <math><mrow><mo><</mo><mi>n</mi></mrow></math>. If <math><mrow><mi>f</mi><mo>∈</mo><msup><mrow><mover><mrow><mi>C</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>r</mi></mrow></msup></mrow></math>, has <math><mrow><mn>2</mn><mi>s</mi></mrow></math>, <math><mrow><mi>s</mi><mo>≥</mo><mn>1</mn></mrow></math>, extremal points in <math><mrow><mo>(</mo><mo>−</mo><mi>π</mi><mo>,</mo><mi>π</mi><mo>]</mo></mrow></math>, denote by <math><mrow><msubsup><mrow><mi>E</mi></mrow><mrow><mi>n</mi></mrow><mrow><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></msubsup><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow><mo>≔</mo><munder><mrow><mo>inf</mo></mrow><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>∈</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>:</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo></mrow></msup><msubsup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>′</mo></mrow></msubsup><mo>≥</mo><mn>0</mn></mrow></munder><mo>‖</mo><mi>f</mi><mo>−</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>‖</mo><mo>,</mo></mrow></math> the error of its best comonotone approximation. We prove, that if <math><mrow><mi>f</mi><mo>∈</mo><msup><mrow><mover><mrow><mi>C</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>r</mi></mrow></msup></mrow></math>, then for either <math><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow></math>, or <math><mrow><mi>m</mi><mo>=</mo><mn>2<","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"299 ","pages":"Article 106015"},"PeriodicalIF":0.9,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139101849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0} 引用次数: 0 引用批量引用Polynomial approximation on disjoint segments and amplification of approximation 不相交线段上的多项式逼近和逼近放大 IF 0.9 3区数学 Q2 Mathematics Journal of Approximation Theory Pub Date : 2024-01-05 DOI: 10.1016/j.jat.2023.106010 Yu. Malykhin , K. Ryutin We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments (see (1)). This problem has important applications in several areas of numerical analysis, complexity theory, quantum algorithms, etc. The one, most relevant for us, is the amplification of approximation method: it allows to construct approximations of higher degree M and better accuracy from the approximations of degree m . 我们为不相交线段结合部上的局部恒定函数（见 (1)）构建了清晰易实现的多项式近似值，其精度足够高。这个问题在数值分析、复杂性理论、量子算法等多个领域都有重要应用。其中与我们最相关的是近似方法的放大：它允许从 m 级的近似值中构造出更高 M 级和更高精度的近似值。求助PDF {"title":"Polynomial approximation on disjoint segments and amplification of approximation","authors":"Yu. Malykhin , K. Ryutin","doi":"10.1016/j.jat.2023.106010","DOIUrl":"10.1016/j.jat.2023.106010","url":null,"abstract":"<div>We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments (see (1)). This problem has important applications in several areas of numerical analysis, complexity theory, quantum algorithms, etc. The one, most relevant for us, is the amplification of approximation method: it allows to construct approximations of higher degree <math><mi>M</mi></math> and better accuracy from the approximations of degree <math><mi>m</mi></math>.</div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"298 ","pages":"Article 106010"},"PeriodicalIF":0.9,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139102000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0} 引用次数: 0 引用批量引用Onesided, intertwining, positive and copositive polynomial approximation with interpolatory constraints 带内插约束的单边、交织、正多项式和共正多项式近似法 IF 0.9 3区数学 Q2 Mathematics Journal of Approximation Theory Pub Date : 2024-01-04 DOI: 10.1016/j.jat.2023.106012 German Dzyubenko , Kirill A. Kopotun Given k \in N, a nonnegative function f \in C^{r} [a, b], r \geq 0, an arbitrary finite collection of points {α_{i}}_{i \in J} \subset [a, b], and a corresponding collection of nonnegative integers {m_{i}}_{i \in J} with 0 \leq m_{i} \leq r, i \in J, is it true that, for sufficiently large n \in N, there exists a polynomial P_{n} of degree n such that (i) | f (x) - P_{n} (x) | \leq c ρ_{n}^{r} (x) ω_{k} (f^{(r)}, ρ_{n} (x); [a, b]), x \in [a, b], where ρ_{n} (x) ≔ n^{- 1} \sqrt{1 - x^{2}} + n^{- 2} and ω_{k} is the classical k th modulus of smoothness. (ii) P^{} 给定 k∈N，一个非负函数 f∈Cr[a,b]，r≥0，一个任意有限点集合 {αi}i∈J⊂[a,b]，以及一个相应的非负整数集合 {mi}i∈J 且 0≤mi≤r、i∈J，那么对于足够大的 n∈N，是否存在一个阶数为 n 的多项式 Pn，使得(i) |f(x)-Pn(x)|≤cρnr(x)ωk(f(r),ρn(x)；[a,b])，x∈[a,b]，其中 ρn(x)≔n-11-x2+n-2，ωk 是经典的第 k 个平滑模。(ii) P(ν)(αi)=f(ν)(αi), for all 0≤ν≤mi and all i∈J,and(iii) either P≥f on [a,b] (onesided approximation), or P≥0 on [a,b] (positive approximation)?我们还证明，一般来说，对于 q≥1 的 q 单调逼近的类似问题，答案是否定的，也就是说，如果 q≥1 时，带有一般内插约束的 q 单调逼近是不可能的。求助PDF {"title":"Onesided, intertwining, positive and copositive polynomial approximation with interpolatory constraints","authors":"German Dzyubenko , Kirill A. Kopotun","doi":"10.1016/j.jat.2023.106012","DOIUrl":"10.1016/j.jat.2023.106012","url":null,"abstract":"<div>Given <math><mrow><mi>k</mi><mo>∈</mo><mi>N</mi></mrow></math>, a nonnegative function <math><mrow><mi>f</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>r</mi></mrow></msup><mrow><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></mrow></mrow></math>, <math><mrow><mi>r</mi><mo>≥</mo><mn>0</mn></mrow></math>, an arbitrary finite collection of points <math><mrow><msub><mrow><mrow><mo>{</mo><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mo>}</mo></mrow></mrow><mrow><mi>i</mi><mo>∈</mo><mi>J</mi></mrow></msub><mo>⊂</mo><mrow><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></mrow></mrow></math>, and a corresponding collection of nonnegative integers <math><msub><mrow><mrow><mo>{</mo><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mo>}</mo></mrow></mrow><mrow><mi>i</mi><mo>∈</mo><mi>J</mi></mrow></msub></math> with <math><mrow><mn>0</mn><mo>≤</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>≤</mo><mi>r</mi></mrow></math>, <math><mrow><mi>i</mi><mo>∈</mo><mi>J</mi></mrow></math>, is it true that, for sufficiently large <math><mrow><mi>n</mi><mo>∈</mo><mi>N</mi></mrow></math>, there exists a polynomial <math><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math> of degree <math><mi>n</mi></math> such that(i) <math><mrow><mrow><mo>|</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>−</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>|</mo></mrow><mo>≤</mo><mi>c</mi><msubsup><mrow><mi>ρ</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>r</mi></mrow></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>f</mi></mrow><mrow><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></msup><mo>,</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>;</mo><mrow><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></mrow><mo>)</mo></mrow></mrow></math>, <math><mrow><mi>x</mi><mo>∈</mo><mrow><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></mrow></mrow></math>, where <math><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mi>n</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>≔</mo><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><msqrt><mrow><mn>1</mn><mo>−</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msqrt><mo>+</mo><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></math> and <math><msub><mrow><mi>ω</mi></mrow><mrow><mi>k</mi></mrow></msub></math> is the classical <math><mi>k</mi></math>th modulus of smoothness.(ii) <math><mrow><msup><mrow><mi>P</mi></mrow><mrow><mrow","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"299 ","pages":"Article 106012"},"PeriodicalIF":0.9,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139093119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0} 引用次数: 0 引用批量引用 Is hyperinterpolation efficient in the approximation of singular and oscillatory functions? 超插值是否能有效逼近奇异函数和振荡函数？ IF 0.9 3区数学 Q2 Mathematics Journal of Approximation Theory Pub Date : 2024-01-04 DOI: 10.1016/j.jat.2023.106013 Congpei An , Hao-Ning Wu Singular and oscillatory functions play a crucial role in various applications, and their approximation is crucial for solving applied mathematics problems efficiently. Hyperinterpolation is a discrete projection method approximating functions with the L^{2} orthogonal projection coefficients obtained by numerical integration. However, this approach may be inefficient for approximating singular and oscillatory functions, requiring a large number of integration points to achieve satisfactory accuracy. To address this issue, we propose a new approximation scheme in this paper, called efficient hyperinterpolation, which leverages the product-integration methods to attain the desired accuracy with fewer numerical integration points than the original scheme. We provide theorems that explain the superiority of efficient hyperinterpolation over the original scheme in approximating such functions belonging to L^{1}, L^{2}, and continuous function spaces, respectively, and demonstrate through numerical experiments on the interval and the sphere that our approach outperforms the original method in terms of accuracy when using a limited number of integration points. 奇异函数和振荡函数在各种应用中发挥着重要作用，对它们进行逼近对于高效解决应用数学问题至关重要。超插值是一种离散投影方法，通过数值积分得到的 L2 正交投影系数来逼近函数。然而，这种方法在逼近奇异函数和振荡函数时可能效率不高，需要大量积分点才能达到令人满意的精度。为了解决这个问题，我们在本文中提出了一种新的近似方案，称为高效超插值，它利用乘积积分法，以比原始方案更少的数值积分点达到所需的精度。我们提供的定理解释了高效超插值在逼近分别属于 L1(Ω)、L2(Ω) 和 C(Ω) 空间的函数时优于原始方案的原因，并通过区间和球面上的数值实验证明，当使用有限数量的积分点时，我们的方法在精度上优于原始方法。求助PDF {"title":"Is hyperinterpolation efficient in the approximation of singular and oscillatory functions?","authors":"Congpei An , Hao-Ning Wu","doi":"10.1016/j.jat.2023.106013","DOIUrl":"10.1016/j.jat.2023.106013","url":null,"abstract":"<div>Singular and oscillatory functions play a crucial role in various applications, and their approximation is crucial for solving applied mathematics problems efficiently. Hyperinterpolation is a discrete projection method approximating functions with the <math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math> orthogonal projection coefficients obtained by numerical integration. However, this approach may be inefficient for approximating singular and oscillatory functions, requiring a large number of integration points to achieve satisfactory accuracy. To address this issue, we propose a new approximation scheme in this paper, called efficient hyperinterpolation, which leverages the product-integration methods to attain the desired accuracy with fewer numerical integration points than the original scheme. We provide theorems that explain the superiority of efficient hyperinterpolation over the original scheme in approximating such functions belonging to <math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math>, <math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math>, and continuous function spaces, respectively, and demonstrate through numerical experiments on the interval and the sphere that our approach outperforms the original method in terms of accuracy when using a limited number of integration points.</div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"299 ","pages":"Article 106013"},"PeriodicalIF":0.9,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0} 引用次数: 0 引用批量引用 On some identities for confluent hypergeometric functions and Bessel functions 关于汇合超几何函数和贝塞尔函数的一些同义词 IF 0.9 3区数学 Q2 Mathematics Journal of Approximation Theory Pub Date : 2024-01-03 DOI: 10.1016/j.jat.2023.106014 Yoshitaka Okuyama Mathematical functions, which often appear in mathematical analysis, are referred to as special functions and have been studied over hundreds of years. Many books and dictionaries are available that describe their properties and serve as a foundation of current science. In this paper, we find a new integral representation of the Whittaker function of the first kind and show a relevant summation formula for Kummer’s confluent hypergeometric functions. We also perform the specifications of our identities to link to known and new results. 在数学分析中经常出现的数学函数被称为特殊函数，其研究已有数百年的历史。许多书籍和字典都描述了它们的性质，是当前科学的基础。在本文中，我们找到了惠特克函数第一类的新积分表示，并展示了库默尔汇交超几何函数的相关求和公式。我们还对我们的标识进行了规范，以便与已知结果和新结果联系起来。求助PDF {"title":"On some identities for confluent hypergeometric functions and Bessel functions","authors":"Yoshitaka Okuyama","doi":"10.1016/j.jat.2023.106014","DOIUrl":"10.1016/j.jat.2023.106014","url":null,"abstract":"<div>Mathematical functions, which often appear in mathematical analysis, are referred to as special functions and have been studied over hundreds of years. Many books and dictionaries are available that describe their properties and serve as a foundation of current science. In this paper, we find a new integral representation of the Whittaker function of the first kind and show a relevant summation formula for Kummer’s confluent hypergeometric functions. We also perform the specifications of our identities to link to known and new results.</div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"298 ","pages":"Article 106014"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0} 引用次数: 0 引用批量引用 Onesided Korovkin approximation 单侧科洛夫金近似 IF 0.9 3区数学 Q2 Mathematics Journal of Approximation Theory Pub Date : 2024-01-03 DOI: 10.1016/j.jat.2023.106011 Michele Campiti In this paper we study in detail some characterizations of Korovkin closures and we also introduce the notions of onesided upper and lower Korovkin closures. We provide some complete characterizations of these new closures which separate the roles of approximating functions in a Korovkin system. We also present some new characterizations of the classical Korovkin closure in spaces of integrable functions. Again we can introduce and characterize the upper and lower Korovkin closures. Finally, we provide some examples which justify the interest in these new closures. 在本文中，我们详细研究了科洛夫金闭包的一些特征，还引入了单面上科洛夫金闭包和单面下科洛夫金闭包的概念。我们提供了这些新闭包的一些完整特征，它们区分了近似函数在科洛夫金系统中的作用。我们还介绍了可积分函数空间中经典科洛夫金闭合的一些新特征。同样，我们可以引入并描述上科罗夫金闭包和下科罗夫金闭包。最后，我们将举例说明这些新闭包的意义。下载PDF {"title":"Onesided Korovkin approximation","authors":"Michele Campiti","doi":"10.1016/j.jat.2023.106011","DOIUrl":"10.1016/j.jat.2023.106011","url":null,"abstract":"<div>In this paper we study in detail some characterizations of Korovkin closures and we also introduce the notions of onesided upper and lower Korovkin closures. We provide some complete characterizations of these new closures which separate the roles of approximating functions in a Korovkin system. We also present some new characterizations of the classical Korovkin closure in spaces of integrable functions. Again we can introduce and characterize the upper and lower Korovkin closures. Finally, we provide some examples which justify the interest in these new closures.</div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"298 ","pages":"Article 106011"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021904523001491/pdfft?md5=c52ebe4199164b358a170c0ce8a2ccd0&pid=1-s2.0-S0021904523001491-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0} 引用次数: 0 引用批量引用 Protein Carbonyl, Lipid Peroxidation, Glutathione and Enzymatic Antioxidant Status in Male Wistar Brain Sub-regions After Dietary Copper Deficiency. 饮食缺铜后雄性 Wistar 脑亚区域的蛋白质羰基、脂质过氧化、谷胱甘肽和酶抗氧化状态 IF 0.9 3区数学 Q2 MATHEMATICS Journal of Approximation Theory Pub Date : 2024-01-01 Epub Date: 2022-10-27 DOI: 10.1007/s12291-022-01093-1 Ankita Rajendra Kurup, Neena Nair Copper a quintessential transitional metal is required for development and function of normal brain and its deficiency has been associated with impairments in brain function. The present study investigates the effects of dietary copper deficiency on brain sub-regions of male Wistar rats for 2-, 4- and 6-week. Pre-pubertal rats were divided into four groups: negative control (NC), copper control (CC), pairfed (PF) and copper deficient (CD). In brain sub regions total protein concentration, glutathione concentration and Cu-Zn SOD activity were down regulated after 2-, 4- and 6 weeks compared to controls and PF groups. Significant increase in brain sub regions was observed in protein carbonyl and lipid peroxidation concentration as well as total SOD, Mn SOD and catalase activities after 2-, 4- and 6 weeks of dietary copper deficiency. Experimental evidences indicate that impaired copper homeostasis has the potential to generate reactive oxygen species enhancing the susceptibility to oxidative stress by inducing up- and down-regulation of non-enzymatic and enzymatic profile studied in brain sub regions causing loss of their normal function which can consequently lead to deterioration of cell structure and death if copper deficiency is prolonged. 铜是一种重要的过渡金属，是正常大脑发育和功能所必需的元素，缺铜会导致大脑功能受损。本研究调查了饮食缺铜对雄性 Wistar 大鼠大脑亚区域的影响，研究时间分别为 2 周、4 周和 6 周。将青春期前的大鼠分为四组：阴性对照组（NC）、铜对照组（CC）、配对喂养组（PF）和铜缺乏组（CD）。与对照组和 PF 组相比，缺铜组在 2、4 和 6 周后大脑亚区的总蛋白浓度、谷胱甘肽浓度和铜锌 SOD 活性都有所下降。缺铜 2 周、4 周和 6 周后，在大脑亚区观察到蛋白质羰基和脂质过氧化物浓度以及总 SOD、锰 SOD 和过氧化氢酶活性显著增加。实验证据表明，铜平衡受损有可能产生活性氧，通过诱导大脑亚区非酶和酶谱的上调和下调，增加对氧化应激的易感性，导致其正常功能丧失，如果长期缺铜，会导致细胞结构恶化和死亡。下载PDF {"title":"Protein Carbonyl, Lipid Peroxidation, Glutathione and Enzymatic Antioxidant Status in Male Wistar Brain Sub-regions After Dietary Copper Deficiency.","authors":"Ankita Rajendra Kurup, Neena Nair","doi":"10.1007/s12291-022-01093-1","DOIUrl":"10.1007/s12291-022-01093-1","url":null,"abstract":"Copper a quintessential transitional metal is required for development and function of normal brain and its deficiency has been associated with impairments in brain function. The present study investigates the effects of dietary copper deficiency on brain sub-regions of male Wistar rats for 2-, 4- and 6-week. Pre-pubertal rats were divided into four groups: negative control (NC), copper control (CC), pairfed (PF) and copper deficient (CD). In brain sub regions total protein concentration, glutathione concentration and Cu-Zn SOD activity were down regulated after 2-, 4- and 6 weeks compared to controls and PF groups. Significant increase in brain sub regions was observed in protein carbonyl and lipid peroxidation concentration as well as total SOD, Mn SOD and catalase activities after 2-, 4- and 6 weeks of dietary copper deficiency. Experimental evidences indicate that impaired copper homeostasis has the potential to generate reactive oxygen species enhancing the susceptibility to oxidative stress by inducing up- and down-regulation of non-enzymatic and enzymatic profile studied in brain sub regions causing loss of their normal function which can consequently lead to deterioration of cell structure and death if copper deficiency is prolonged.","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"2 1","pages":"73-82"},"PeriodicalIF":0.9,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10784247/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74702717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0} 引用次数: 0 引用批量引用 Chebyshev unions of planes, and their approximative and geometric properties 平面的切比雪夫联合及其近似和几何特性 IF 0.9 3区数学 Q2 Mathematics Journal of Approximation Theory Pub Date : 2023-12-30 DOI: 10.1016/j.jat.2023.106009 A.R. Alimov , I.G. Tsar’kov We study approximative and geometric properties of Chebyshev sets composed of at most countably many planes (i.e., closed affine subspaces). We will assume that the union of planes is irreducible, i.e., no plane in this union contains another plane from the union. We show, in particular, that if a Chebyshev subset M of a Banach space X consists of at least two planes, then it is not B -connected (i.e., its intersection with some closed ball is disconnected) and is not \overset{̊}{B} -complete. We also verify that, in reflexive (CLUR) -spaces (and, in particularly, in complete uniformly convex spaces), a set composed of countably many planes is not a Chebyshev set. For finite unions, we show that any finite union of planes (involving at least two planes) is not a Chebyshev set for any norm on the space. Several applications of our results in the spaces C (Q), L^{1} and L^{\infty} are also given. 我们研究由最多可数平面（即封闭仿射子空间）组成的切比雪夫集的近似和几何性质。我们将假定平面的联合是不可还原的，即这个联合中没有一个平面包含联合中的另一个平面。我们将特别证明，如果巴拿赫空间 X 的切比雪夫子集 M 至少由两个平面组成，那么它就不是 B-连接的（即它与某个闭球的交集是断开的），也就不是 B̊-完备的。我们还验证了在反射（CLUR）空间（尤其是在完全均匀凸空间）中，由可数平面组成的集合不是切比雪夫集合。对于有限联合，我们证明了对于空间上的任何规范，任何平面的有限联合（至少涉及两个平面）都不是切比雪夫集合。我们还给出了我们的结果在空间 C(Q)、L1 和 L∞ 中的一些应用。求助PDF {"title":"Chebyshev unions of planes, and their approximative and geometric properties","authors":"A.R. Alimov , I.G. Tsar’kov","doi":"10.1016/j.jat.2023.106009","DOIUrl":"10.1016/j.jat.2023.106009","url":null,"abstract":"<div>We study approximative and geometric properties of Chebyshev sets composed of at most countably many planes (i.e., closed affine subspaces). We will assume that the union of planes is irreducible, i.e., no plane in this union contains another plane from the union. We show, in particular, that if a Chebyshev subset <math><mi>M</mi></math> of a Banach space <math><mi>X</mi></math> consists of at least two planes, then it is not <math><mi>B</mi></math>-connected (i.e., its intersection with some closed ball is disconnected) and is not <math><mover><mrow><mi>B</mi></mrow><mrow><mo>̊</mo></mrow></mover></math>-complete. We also verify that, in reflexive <math><mrow><mo>(</mo><mi>CLUR</mi><mo>)</mo></mrow></math>-spaces (and, in particularly, in complete uniformly convex spaces), a set composed of countably many planes is not a Chebyshev set. For finite unions, we show that any finite union of planes (involving at least two planes) is not a Chebyshev set for any norm on the space. Several applications of our results in the spaces <math><mrow><mi>C</mi><mrow><mo>(</mo><mi>Q</mi><mo>)</mo></mrow></mrow></math>, <math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math> and <math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math> are also given.</div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"298 ","pages":"Article 106009"},"PeriodicalIF":0.9,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0} 引用次数: 0 引用批量引用 An asymptotic development of the Poisson integral for Laguerre polynomial expansions 拉盖尔多项式展开式泊松积分的渐近发展 IF 0.9 3区数学 Q2 Mathematics Journal of Approximation Theory Pub Date : 2023-12-02 DOI: 10.1016/j.jat.2023.106007 Ulrich Abel The purpose of this paper is the study of the rate of convergence of Poisson integrals for Laguerre expansions. The convergence of partial sums of Fourier series of functions in L^{p} spaces was studied, for several classes of orthogonal polynomials. In the Laguerre case Askey and Waigner proved convergence for functions f \in L^{p} (0, + \infty) with 4 / 3 < p < 4 . In this paper we deal with the Poisson integral A_{r} f (0 < r < 1) which arises by applying Abel’s summation method to the Laguerre expansion of the function f . About 50 years ago, Muckenhoupt intensively studied the Poisson integral for the Laguerre and Hermite polynomials. Among other things he proved pointwise convergence, the convergence by norm, and that the Poisson integral is a contraction mapping in L^{p} (0, \infty) . Toczek and Wachnicki gave a Voronovskaja-type theorem by calculating the limit {(1 - r)}^{- 1} ((A_{r} f) (x) - f (x)) as r \to 1^{-}, provided that f^{''} (x) exists. We generalize this formula by deriving a complete asymptotic development. All its coefficients are explicitly given in a concise form. As an application we apply extrapolation methods in order to improve the rate of convergence of (A_{r} f) (x) as r \to 1^{-} . 本文的目的是研究拉盖尔展开下泊松积分的收敛速度。研究了几种正交多项式在Lp空间中的傅里叶级数部分和的收敛性。在Laguerre情况下，Askey和Waigner用4/3<p<4证明了函数f∈l0，+∞的收敛性。在本文中，我们处理了泊松积分Arf0<r<1，它是通过将Abel的求和方法应用于函数f的拉盖尔展开而产生的。大约50年前，Muckenhoupt深入研究了拉盖尔多项式和埃尔米特多项式的泊松积分。除此之外，他还证明了点向收敛，范数收敛，泊松积分是l0，∞上的收缩映射。Toczek和Wachnicki通过计算极限1−r−1Arfx−fx为r→1−，给出了voronovskaja型定理，假设f ' x存在。我们通过推导一个完全渐近展开来推广这个公式。它的所有系数都以简洁的形式显式给出。作为一种应用，我们采用外推方法来提高Arfx在r→1−时的收敛速度。求助PDF {"title":"An asymptotic development of the Poisson integral for Laguerre polynomial expansions","authors":"Ulrich Abel","doi":"10.1016/j.jat.2023.106007","DOIUrl":"https://doi.org/10.1016/j.jat.2023.106007","url":null,"abstract":"<div>The purpose of this paper is the study of the rate of convergence of Poisson integrals for Laguerre expansions. The convergence of partial sums of Fourier series of functions in <math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math> spaces was studied, for several classes of orthogonal polynomials. In the Laguerre case Askey and Waigner proved convergence for functions <math><mrow><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mfenced><mrow><mn>0</mn><mo>,</mo><mo>+</mo><mi>∞</mi></mrow></mfenced></mrow></math> with <math><mrow><mn>4</mn><mo>/</mo><mn>3</mn><mo><</mo><mi>p</mi><mo><</mo><mn>4</mn></mrow></math>. In this paper we deal with the Poisson integral <math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>r</mi></mrow></msub><mi>f</mi></mrow></math>\u0000<math><mfenced><mrow><mn>0</mn><mo><</mo><mi>r</mi><mo><</mo><mn>1</mn></mrow></mfenced></math> which arises by applying Abel’s summation method to the Laguerre expansion of the function <math><mi>f</mi></math>. About 50 years ago, Muckenhoupt intensively studied the Poisson integral for the Laguerre and Hermite polynomials. Among other things he proved pointwise convergence, the convergence by norm, and that the Poisson integral is a contraction mapping in <math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mfenced><mrow><mn>0</mn><mo>,</mo><mi>∞</mi></mrow></mfenced></mrow></math>. Toczek and Wachnicki gave a Voronovskaja-type theorem by calculating the limit <math><mrow><msup><mrow><mfenced><mrow><mn>1</mn><mo>−</mo><mi>r</mi></mrow></mfenced></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mfenced><mrow><mfenced><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>r</mi></mrow></msub><mi>f</mi></mrow></mfenced><mfenced><mrow><mi>x</mi></mrow></mfenced><mo>−</mo><mi>f</mi><mfenced><mrow><mi>x</mi></mrow></mfenced></mrow></mfenced></mrow></math> as <math><mrow><mi>r</mi><mo>→</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msup></mrow></math>, provided that <math><mrow><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo><mo>′</mo></mrow></msup><mfenced><mrow><mi>x</mi></mrow></mfenced></mrow></math> exists. We generalize this formula by deriving a complete asymptotic development. All its coefficients are explicitly given in a concise form. As an application we apply extrapolation methods in order to improve the rate of convergence of <math><mrow><mfenced><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>r</mi></mrow></msub><mi>f</mi></mrow></mfenced><mfenced><mrow><mi>x</mi></mrow></mfenced></mrow></math> as <math><mrow><mi>r</mi><mo>→</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>−</mo></mrow></msup></mrow></math>.</div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"298 ","pages":"Article 106007"},"PeriodicalIF":0.9,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138501441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0} 引用次数: 0 引用批量引用首页上一页 23456789 ... 10 下一页尾页类型全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程数据库全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley 期刊 Journal of Approximation Theory 全部 Acc. 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}
const sLength = (searchCleanArr.join('')).substring(pos).length;
if (sLength === 0 || digitCount / sLength < 0.5) {
return false;
}
return true;
}var clearShow = false;
$(function () {
if ($("#tkeyword").val().trim().length > 0) {
$("#clear").show();
clearShow = true;
}
$("#tkeyword").keydown(function (e) {
var curKey = e.which;
if (curKey == 13) {

}
});
$("#SearchBtn").click(function () {
var keyWordHome = $("#tkeyword").val();
var fullWidthRegex = /[\u3000-\u303F\u3040-\u309F\u30A0-\u30FF\u3100-\u312F\u3130-\u318F\u3190-\u319F\u31A0-\u31BF\u31C0-\u31EF\u31F0-\u31FF\u3200-\u32FF\u3300-\u33FF\uFF00-\uFFEF\u4E00-\u9FFF]/;

if (keyWordHome.trim().length == 0) {
alert("请输入搜索关键字");
$("#tkeyword").focus();
return;
}
if (/[\u4e00-\u9fa5]/.test($("#tkeyword").val())) {
if ($("#tkeyword").val().trim().length > 200) {
alert("关键词长度不能大于200个字符");
return;
}
}
else {
if ($("#tkeyword").val().trim().length > 500) {
alert("关键词长度不能大于500个字符");
return;
}
}
if (fullWidthRegex.test(keyWordHome)) {
keyWordHome = toHalfWidth(keyWordHome);
}

var regex = /\b(10[.][0-9]{4,}(?:[.][0-9]+)*\/(?:(?![\|"&\'])\S)+)(?:\+?|\b)/g;
const optionarr = keyWordHome.trim().match(regex);
if ((optionarr != undefined && optionarr.length > 0) || isPaperGo(keyWordHome.trim())) {
window.open('/literature/literaturelist?keyword=' + encodeURIComponent(keyWordHome));
}
else {
window.location.href = '/literature/literaturelist?keyword=' + encodeURIComponent(keyWordHome);
}
});
$(":text.ssi").unbind().keyup(function (event) {
var which = event.which;
if (which != 13) {
if ($("[data-module='scisearch']").length > 0) {
$("[data-module='scisearch']").attr("data-search-value", $(this).val());
}
}
else {
$("#SearchBtn").click();
}
});
$(":text.ssi").on('input', function () {
if ($("[data-module='scisearch']").length > 0) {
$("[data-module='scisearch']").attr("data-search-value", $(this).val());
}
});

$("#clear").click(function () {
$("#tkeyword").val("");
$("#clear").hide();
clearShow = false;
$("#tkeyword").focus();
});

$("#tkeyword").keyup(function () {
if ($(this).val().trim().length > 0) {
if (!clearShow) {
$("#clear").show();
clearShow = true;
}
}
else {
if (clearShow) {
$("#clear").hide();
clearShow = false;
}
}
});

$("#tkeyword").change(function () {
if ($(this).val().trim().length > 0) {
if (!clearShow) {
$("#clear").show();
clearShow = true;
}
}
else {
if (clearShow) {
$("#clear").hide();
clearShow = false;
}
}
})

if (getCookie("userName") == null) {
if (getCookie("_sci_uid") == null) {
var uuidstr = getuuid();
setCookie("_sci_uid", "sci_" + uuidstr, 9999);
}
}
});

function isPaperGo(s) {
let pos = 0;
let digitCount = 0;
let flag = false;
const searchCleanArr = s.split(/[., ]/).map(item => item.trim()).filter(item => item !== '');
for (const item of searchCleanArr) {
if (!flag) {
if (!isNaN(parseInt(item[0]))) {
flag = !flag;
} else {
pos += item.length;
}
} else {
for (const i of item) {
if (!isNaN(i)) {
digitCount++;
}
}
}
}
const sLength = (searchCleanArr.join('')).substring(pos).length;
if (sLength === 0 || digitCount / sLength < 0.5) {
return false;
}
return true;
}$