Pub Date : 2024-03-06DOI: 10.1134/s0081543823050152
Yirui Zhao, Yoshihiro Sawano, Jin Tao, Dachun Yang, Wen Yuan
Abstract
Bourgain–Morrey spaces (mathcal{M}^p_{q,r}(mathbb R^n)), generalizing what was introduced by J. Bourgain, play an important role in the study related to the Strichartz estimate and the nonlinear Schrödinger equation. In this article, via adding an extra exponent (tau), the authors creatively introduce a new class of function spaces, called Besov–Bourgain–Morrey spaces (mathcal{M}dot{B}^{p,tau}_{q,r}(mathbb R^n)), which is a bridge connecting Bourgain–Morrey spaces (mathcal{M}^p_{q,r}(mathbb R^n)) with amalgam-type spaces ((L^q,ell^r)^p(mathbb R^n)). By making full use of the Fatou property of block spaces in the weak local topology of (L^{q'}(mathbb R^n)), the authors give both predual and dual spaces of (mathcal{M}dot{B}^{p,tau}_{q,r}(mathbb R^n)). Applying these properties and the Calderón product, the authors also establish the complex interpolation of (mathcal{M}dot{B}^{p,tau}_{q,r}(mathbb R^n)). Via fully using fine geometrical properties of dyadic cubes, the authors then give an equivalent norm of (|kern1pt{cdot}kern1pt|_{mathcal{M}dot{B}^{p,tau}_{q,r}(mathbb R^n)}) having an integral expression, which further induces a boundedness criterion of operators on (mathcal{M}dot{B}^{p,tau}_{q,r}(mathbb R^n)). Applying this criterion, the authors obtain the boundedness on (mathcal{M}dot{B}^{p,tau}_{q,r}(mathbb R^n)) of classical operators including the Hardy–Littlewood maximal operator, the fractional integral, and the Calderón–Zygmund operator.
{"title":"Bourgain–Morrey Spaces Mixed with Structure of Besov Spaces","authors":"Yirui Zhao, Yoshihiro Sawano, Jin Tao, Dachun Yang, Wen Yuan","doi":"10.1134/s0081543823050152","DOIUrl":"https://doi.org/10.1134/s0081543823050152","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Bourgain–Morrey spaces <span>(mathcal{M}^p_{q,r}(mathbb R^n))</span>, generalizing what was introduced by J. Bourgain, play an important role in the study related to the Strichartz estimate and the nonlinear Schrödinger equation. In this article, via adding an extra exponent <span>(tau)</span>, the authors creatively introduce a new class of function spaces, called Besov–Bourgain–Morrey spaces <span>(mathcal{M}dot{B}^{p,tau}_{q,r}(mathbb R^n))</span>, which is a bridge connecting Bourgain–Morrey spaces <span>(mathcal{M}^p_{q,r}(mathbb R^n))</span> with amalgam-type spaces <span>((L^q,ell^r)^p(mathbb R^n))</span>. By making full use of the Fatou property of block spaces in the weak local topology of <span>(L^{q'}(mathbb R^n))</span>, the authors give both predual and dual spaces of <span>(mathcal{M}dot{B}^{p,tau}_{q,r}(mathbb R^n))</span>. Applying these properties and the Calderón product, the authors also establish the complex interpolation of <span>(mathcal{M}dot{B}^{p,tau}_{q,r}(mathbb R^n))</span>. Via fully using fine geometrical properties of dyadic cubes, the authors then give an equivalent norm of <span>(|kern1pt{cdot}kern1pt|_{mathcal{M}dot{B}^{p,tau}_{q,r}(mathbb R^n)})</span> having an integral expression, which further induces a boundedness criterion of operators on <span>(mathcal{M}dot{B}^{p,tau}_{q,r}(mathbb R^n))</span>. Applying this criterion, the authors obtain the boundedness on <span>(mathcal{M}dot{B}^{p,tau}_{q,r}(mathbb R^n))</span> of classical operators including the Hardy–Littlewood maximal operator, the fractional integral, and the Calderón–Zygmund operator. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"2 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140054770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-06DOI: 10.1134/s0081543823050127
D. M. Stolyarov
Abstract
We show that the zero smoothness Besov space (B_{p,q}^{0,1}) does not embed into the Lorentz space (L_{p,q}) unless (p=q); here (p,qin (1,infty)). This answers in the negative a question posed by O. V. Besov.
Abstract 我们证明了零光滑度贝索夫空间（B_{p,q}^{0,1}）不会嵌入洛伦兹空间（L_{p,q}），除非 (p=q)；这里是 (p,qin(1,infty))。这从反面回答了 O. V. Besov 提出的一个问题。
{"title":"On Embedding of Besov Spaces of Zero Smoothness into Lorentz Spaces","authors":"D. M. Stolyarov","doi":"10.1134/s0081543823050127","DOIUrl":"https://doi.org/10.1134/s0081543823050127","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We show that the zero smoothness Besov space <span>(B_{p,q}^{0,1})</span> does not embed into the Lorentz space <span>(L_{p,q})</span> unless <span>(p=q)</span>; here <span>(p,qin (1,infty))</span>. This answers in the negative a question posed by O. V. Besov. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"46 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-06DOI: 10.1134/s0081543823050097
S. V. Konyagin
Abstract
A. N. Kolmogorov’s famous theorem of 1925 implies that the partial sums of the Fourier series of any integrable function (f) of one variable converge to it in (L^p) for all (pin(0,1)). It is known that this does not hold true for functions of several variables. In this paper we prove that, nevertheless, for any function of several variables there is a subsequence of Pringsheim partial sums that converges to the function in (L^p) for all (pin(0,1)). At the same time, in a fairly general case, when we take the partial sums of the Fourier series of a function of several variables over an expanding system of index sets, there exists a function for which the absolute values of a certain subsequence of these partial sums tend to infinity almost everywhere. This is so, in particular, for a system of dilations of a fixed bounded convex body and for hyperbolic crosses.
Abstract A. N. Kolmogorov 1925 年的著名定理意味着，对于所有的 (pin(0,1)) ，一个变量的任何可积分函数 (f) 的傅里叶级数的部分和都会收敛到 (L^p) 中。众所周知，这对于多变量函数来说并不成立。在本文中，我们证明了，尽管如此，对于任何几个变量的函数，都存在一个普林塞姆偏和子序列，对于所有的（pin(0,1)），这个子序列都收敛到了(L^p)中的函数。与此同时，在一种相当普遍的情况下，当我们求几个变量的函数在一个扩展的索引集系统上的傅里叶级数的偏和时，存在这样一个函数，对它来说，这些偏和的某个子序列的绝对值几乎在所有地方都趋向于无穷大。对于固定有界凸体的扩张系统和双曲交叉来说，尤其如此。
{"title":"On Pringsheim Convergence of a Subsequence of Partial Sums of a Multiple Trigonometric Fourier Series","authors":"S. V. Konyagin","doi":"10.1134/s0081543823050097","DOIUrl":"https://doi.org/10.1134/s0081543823050097","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A. N. Kolmogorov’s famous theorem of 1925 implies that the partial sums of the Fourier series of any integrable function <span>(f)</span> of one variable converge to it in <span>(L^p)</span> for all <span>(pin(0,1))</span>. It is known that this does not hold true for functions of several variables. In this paper we prove that, nevertheless, for any function of several variables there is a subsequence of Pringsheim partial sums that converges to the function in <span>(L^p)</span> for all <span>(pin(0,1))</span>. At the same time, in a fairly general case, when we take the partial sums of the Fourier series of a function of several variables over an expanding system of index sets, there exists a function for which the absolute values of a certain subsequence of these partial sums tend to infinity almost everywhere. This is so, in particular, for a system of dilations of a fixed bounded convex body and for hyperbolic crosses. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"7 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-06DOI: 10.1134/s0081543823050103
V. G. Krotov
Abstract
A number of statements similar to the Marcinkiewicz interpolation theorem are presented. The difference from the classical forms of this theorem is that the spaces of integrable functions are replaced by certain classes of functions that are extensions of various Hardy spaces.
{"title":"Interpolation of Operators in Hardy-Type Spaces","authors":"V. G. Krotov","doi":"10.1134/s0081543823050103","DOIUrl":"https://doi.org/10.1134/s0081543823050103","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A number of statements similar to the Marcinkiewicz interpolation theorem are presented. The difference from the classical forms of this theorem is that the spaces of integrable functions are replaced by certain classes of functions that are extensions of various Hardy spaces. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"12 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140054756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-06DOI: 10.1134/s0081543823050085
Winfried Sickel
Abstract
Let (E) be a domain in (mathbb R^d). We investigate the regularity of the characteristic function (mathcal X_E) depending on the behavior of the (delta)-neighborhoods of the boundary of (E). The regularity is measured in terms of the Nikol’skii–Besov and Lizorkin–Triebel spaces.
Abstract Let (E) be a domain in (mathbb R^d).我们研究了特征函数 (mathcal X_E) 的正则性，它取决于 (E) 边界的 (delta)-neighborhoods 的行为。正则性是通过尼克尔斯基-贝索夫空间和利佐金-特里贝尔空间来衡量的。
{"title":"On the Regularity of Characteristic Functions of Weakly Exterior Thick Domains","authors":"Winfried Sickel","doi":"10.1134/s0081543823050085","DOIUrl":"https://doi.org/10.1134/s0081543823050085","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Let <span>(E)</span> be a domain in <span>(mathbb R^d)</span>. We investigate the regularity of the characteristic function <span>(mathcal X_E)</span> depending on the behavior of the <span>(delta)</span>-neighborhoods of the boundary of <span>(E)</span>. The regularity is measured in terms of the Nikol’skii–Besov and Lizorkin–Triebel spaces. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"72 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140054773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-06DOI: 10.1134/s0081543823050140
Hans Triebel
Abstract
The paper deals with some recent assertions about truncations (fmapsto |f|) and compositions (fmapsto gcirc f) in the spaces (A^s_{p,q}(mathbb R^n)), (Ain{B,F}).
{"title":"Truncations and Compositions in Function Spaces","authors":"Hans Triebel","doi":"10.1134/s0081543823050140","DOIUrl":"https://doi.org/10.1134/s0081543823050140","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The paper deals with some recent assertions about truncations <span>(fmapsto |f|)</span> and compositions <span>(fmapsto gcirc f)</span> in the spaces <span>(A^s_{p,q}(mathbb R^n))</span>, <span>(Ain{B,F})</span>. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"4 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140054750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-06DOI: 10.1134/s0081543823050024
Alexander Bendikov, Alexander Grigor’yan, Stanislav Molchanov
Abstract
We consider the operator (H=L+V) that is a perturbation of the Taibleson–Vladimirov operator (L=mathfrak{D}^alpha) by a potential (V(x)=b|x|^{-alpha}), where (alpha>0) and (bgeq b_*). We prove that the operator (H) is closable and its minimal closure is a nonnegative definite self-adjoint operator (where the critical value (b_*) depends on (alpha)). While the operator (H) is nonnegative definite, the potential (V(x)) may well take negative values as (b_*<0) for all (0<alpha<1). The equation (Hu=v) admits a Green function (g_H(x,y)), that is, the integral kernel of the operator (H^{-1}). We obtain sharp lower and upper bounds on the ratio of the Green functions (g_H(x,y)) and (g_L(x,y)).
Abstract We consider the operator (H=L+V) that is a perturbation of the Taibleson-Vladimirov operator (L=mathfrak{D}^alpha) by a potential (V(x)=b|x|^{-alpha}) where (alpha>0) and(bgeq b_*).我们证明了算子(H) 是可闭的，并且它的最小闭包是一个非负定值的自交算子（其中临界值(b_*) 取决于(alpha)）。虽然算子(H)是非负定的，但对于所有的(0<alpha<1)，势(V(x))很可能取负值，因为(b_*<0)是负值。方程 （Hu=v）有一个格林函数 （g_H(x,y)），即算子 （H^{-1}）的积分核。我们得到了格林函数 （g_H(x,y)）和 （g_L(x,y)）比率的尖锐下界和上界。
{"title":"Hierarchical Schrödinger Operators with Singular Potentials","authors":"Alexander Bendikov, Alexander Grigor’yan, Stanislav Molchanov","doi":"10.1134/s0081543823050024","DOIUrl":"https://doi.org/10.1134/s0081543823050024","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the operator <span>(H=L+V)</span> that is a perturbation of the Taibleson–Vladimirov operator <span>(L=mathfrak{D}^alpha)</span> by a potential <span>(V(x)=b|x|^{-alpha})</span>, where <span>(alpha>0)</span> and <span>(bgeq b_*)</span>. We prove that the operator <span>(H)</span> is closable and its minimal closure is a nonnegative definite self-adjoint operator (where the critical value <span>(b_*)</span> depends on <span>(alpha)</span>). While the operator <span>(H)</span> is nonnegative definite, the potential <span>(V(x))</span> may well take negative values as <span>(b_*<0)</span> for all <span>(0<alpha<1)</span>. The equation <span>(Hu=v)</span> admits a Green function <span>(g_H(x,y))</span>, that is, the integral kernel of the operator <span>(H^{-1})</span>. We obtain sharp lower and upper bounds on the ratio of the Green functions <span>(g_H(x,y))</span> and <span>(g_L(x,y))</span>. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"118 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-06DOI: 10.1134/s0081543823050061
Ryan Gibara, Nageswari Shanmugalingam
Abstract
In this paper we fix (1le p<infty) and consider ((Omega,d,mu)) to be an unbounded, locally compact, non-complete metric measure space equipped with a doubling measure (mu) supporting a (p)-Poincaré inequality such that (Omega) is a uniform domain in its completion (overlineOmega). We realize the trace of functions in the Dirichlet–Sobolev space (D^{1,p}(Omega)) on the boundary (partialOmega) as functions in the homogeneous Besov space (Hkern-1pt B^alpha_{p,p}(partialOmega)) for suitable (alpha); here, (partialOmega) is equipped with a non-atomic Borel regular measure (nu). We show that if (nu) satisfies a (theta)-codimensional condition with respect to (mu) for some (0<theta<p), then there is a bounded linear trace operator (T colon, D^{1,p}(Omega)to Hkern-1pt B^{1-theta/p}(partialOmega)) and a bounded linear extension operator (E colon, Hkern-1pt B^{1-theta/p}(partialOmega)to D^{1,p}(Omega)) that is a right-inverse of (T).
Abstract In this paper we fix(1le p<infty) and consider ((Omega,d,mu)) to be an unbounded, locally compact, non-complete metric measure space equipped with a doubling measure (mu) supporting a (p)-Poincaré inequality such that (Omega) is a uniform domain in its completion (overlineOmega).我们将边界 (partialOmega) 上的 Dirichlet-Sobolev 空间 (D^{1,p}(Omega)) 中的函数的迹作为同质 Besov 空间 (Hkern-1pt B^alpha_{p,p}(partialOmega)) 中的函数来实现，对于合适的 (alpha)；这里，(partialOmega) 配备了一个非原子的波尔正则量度(nu)。我们证明，如果(nu)满足一个关于(mu)的(theta)-codimensional条件，对于某个(0<theta<；p），那么存在一个有界线性迹算子（T colon, D^{1,p}(Omega)to Hkern-1pt B^{1-theta/p}(partialOmega)) 和一个有界线性扩展算子（E colon、Hkern-1pt B^{1-theta/p}(partialOmega)to D^{1,p}(Omega)) 是 (T)的右逆。
{"title":"Trace and Extension Theorems for Homogeneous Sobolev and Besov Spaces for Unbounded Uniform Domains in Metric Measure Spaces","authors":"Ryan Gibara, Nageswari Shanmugalingam","doi":"10.1134/s0081543823050061","DOIUrl":"https://doi.org/10.1134/s0081543823050061","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In this paper we fix <span>(1le p<infty)</span> and consider <span>((Omega,d,mu))</span> to be an unbounded, locally compact, non-complete metric measure space equipped with a doubling measure <span>(mu)</span> supporting a <span>(p)</span>-Poincaré inequality such that <span>(Omega)</span> is a uniform domain in its completion <span>(overlineOmega)</span>. We realize the trace of functions in the Dirichlet–Sobolev space <span>(D^{1,p}(Omega))</span> on the boundary <span>(partialOmega)</span> as functions in the homogeneous Besov space <span>(Hkern-1pt B^alpha_{p,p}(partialOmega))</span> for suitable <span>(alpha)</span>; here, <span>(partialOmega)</span> is equipped with a non-atomic Borel regular measure <span>(nu)</span>. We show that if <span>(nu)</span> satisfies a <span>(theta)</span>-codimensional condition with respect to <span>(mu)</span> for some <span>(0<theta<p)</span>, then there is a bounded linear trace operator <span>(T colon, D^{1,p}(Omega)to Hkern-1pt B^{1-theta/p}(partialOmega))</span> and a bounded linear extension operator <span>(E colon, Hkern-1pt B^{1-theta/p}(partialOmega)to D^{1,p}(Omega))</span> that is a right-inverse of <span>(T)</span>. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"16 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140890037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Integral Representations and Embeddings of Spaces of Functions of Positive Smoothness on a Hölder Domain","authors":"O. V. Besov","doi":"10.1134/s0081543823050036","DOIUrl":"https://doi.org/10.1134/s0081543823050036","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We prove embedding theorems for spaces of functions of positive smoothness defined on a Hölder domain of <span>(n)</span>-dimensional Euclidean space. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"102 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140054652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-06DOI: 10.1134/s0081543823050115
G. G. Magaril-Il’yaev, E. O. Sivkova
Abstract
Given a one-parameter family of operators on the manifold (mathbb R^ntimesmathbb T^m), we solve the problem of the best recovery of an operator for a given value of the parameter from inaccurate data on the operators for other values of the parameter from a certain compact set. We construct a family of best recovery methods. As a consequence, we obtain families of best recovery methods for the solutions of the heat equation and the Dirichlet problem for a half-space.
Abstract Given a one-parameter family of operators on the manifold (mathbb R^ntimesmathbb T^m)， we solve the problem of the best recovery of an operator for a given value of the parameter from inaccurate data on the operators for other values of the parameter from a certain compact set.我们构建了一个最佳复原方法族。因此，我们得到了半空间热方程和迪里夏特问题解的最佳复原方法族。
{"title":"On the Best Recovery of a Family of Operators on the Manifold $$mathbb R^ntimesmathbb T^m$$","authors":"G. G. Magaril-Il’yaev, E. O. Sivkova","doi":"10.1134/s0081543823050115","DOIUrl":"https://doi.org/10.1134/s0081543823050115","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Given a one-parameter family of operators on the manifold <span>(mathbb R^ntimesmathbb T^m)</span>, we solve the problem of the best recovery of an operator for a given value of the parameter from inaccurate data on the operators for other values of the parameter from a certain compact set. We construct a family of best recovery methods. As a consequence, we obtain families of best recovery methods for the solutions of the heat equation and the Dirichlet problem for a half-space. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"281 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140054749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号