Abstract Let 0 p α β ⩽2 π . We prove that for trigonometric polynomials s n of degree ⩽ n , we have[formula]where c is independent of α , β , n , s n . The essential feature is the uniformity in α and β of the estimate. The result may be viewed as an L p form of Videnskii's inequalities.
设0 p α β≥2 π。我们证明了对于阶次为n的三角多项式s n，我们有[公式]，其中c与α， β， n, sn无关。其基本特征是估计的α和β的均匀性。这个结果可以看作是维登斯基不等式的一个L - p形式。
{"title":"Lp Markov-Bernstein Inequalities on Arcs of the Circle","authors":"D. Lubinsky","doi":"10.1006/jath.2000.3502","DOIUrl":"https://doi.org/10.1006/jath.2000.3502","url":null,"abstract":"Abstract Let 0 p α β ⩽2 π . We prove that for trigonometric polynomials s n of degree ⩽ n , we have[formula]where c is independent of α , β , n , s n . The essential feature is the uniformity in α and β of the estimate. The result may be viewed as an L p form of Videnskii's inequalities.","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125578974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a new method to construct finite orthogonal quadrature filters using convolution kernels and show that every filter with value 1 at the origin can be obtained from an even nonnegative kernel. We apply the method to estimate the optimal frequency localization of finite filters. The frequency localization @c"p of a finite filter m"0 is given by the distance in L^p-norm between |m"0|^2 and the Shannon low-pass filter. For each N>0 there is a filter m^N"0 of length 2N minimizing the value of @c"p. We prove that for such a minimizing sequence we have @c^p"p(m^N"0)=O(1/N), 1=
{"title":"On the Construction and Frequency Localization of Finite Orthogonal Quadrature Filters","authors":"M. Nielsen","doi":"10.1006/jath.2000.3514","DOIUrl":"https://doi.org/10.1006/jath.2000.3514","url":null,"abstract":"We introduce a new method to construct finite orthogonal quadrature filters using convolution kernels and show that every filter with value 1 at the origin can be obtained from an even nonnegative kernel. We apply the method to estimate the optimal frequency localization of finite filters. The frequency localization @c\"p of a finite filter m\"0 is given by the distance in L^p-norm between |m\"0|^2 and the Shannon low-pass filter. For each N>0 there is a filter m^N\"0 of length 2N minimizing the value of @c\"p. We prove that for such a minimizing sequence we have @c^p\"p(m^N\"0)=O(1/N), 1=","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"119023345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The exact values of Kolmogorov n-widths have been calculated for two basic classes of functions. They are, on the one hand, classes of real functions defined by variation diminishing kernels and similar classes of analytic functions, and, on the other hand, classes of functions in a Hilbert space which are elliptical cylinders or generalized octahedra. This second case is surveyed and new results are presented. For n-widths of ellipsoids, elliptic cylinders, and generalized octahedra, upper bounds for the n-widths are based on the Fourier method. The lower bounds are based on the method of ''embedded balls'' for ellipsoids and the method of averaging for generalized octahedra. General theorems concerning elliptical cylinders and generalized octahedra are proved, various corollaries from these general theorems are considered, and some additional problems (average n-widths, extremal spaces for an ellipsoids and octahedra, etc.) are discussed.
{"title":"On Exact Values of n-Widths in a Hilbert Space","authors":"G. Magaril-Il'yaev, K. Osipenko, V. Tikhomirov","doi":"10.1006/jath.2000.3497","DOIUrl":"https://doi.org/10.1006/jath.2000.3497","url":null,"abstract":"The exact values of Kolmogorov n-widths have been calculated for two basic classes of functions. They are, on the one hand, classes of real functions defined by variation diminishing kernels and similar classes of analytic functions, and, on the other hand, classes of functions in a Hilbert space which are elliptical cylinders or generalized octahedra. This second case is surveyed and new results are presented. For n-widths of ellipsoids, elliptic cylinders, and generalized octahedra, upper bounds for the n-widths are based on the Fourier method. The lower bounds are based on the method of ''embedded balls'' for ellipsoids and the method of averaging for generalized octahedra. General theorems concerning elliptical cylinders and generalized octahedra are proved, various corollaries from these general theorems are considered, and some additional problems (average n-widths, extremal spaces for an ellipsoids and octahedra, etc.) are discussed.","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126200633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider a quadrature rule for Cauchy integrals of the form I(wf;s)=[formula]w(t)f(t)/(t-s)dt, -1-1/2. Using the change of variables t=cosy, s=cosx and subtracting out the singularity, we propose a trigonometric quadrature rule. We obtain the error bounds independent of the set of values of poles and construct an automatic quadrature of nonadaptive type.
{"title":"A Trigonometric Quadrature Rule for Cauchy Integrals with Jacobi Weight","authors":"Philsu Kim","doi":"10.1006/jath.2000.3513","DOIUrl":"https://doi.org/10.1006/jath.2000.3513","url":null,"abstract":"In this paper, we consider a quadrature rule for Cauchy integrals of the form I(wf;s)=[formula]w(t)f(t)/(t-s)dt, -1-1/2. Using the change of variables t=cosy, s=cosx and subtracting out the singularity, we propose a trigonometric quadrature rule. We obtain the error bounds independent of the set of values of poles and construct an automatic quadrature of nonadaptive type.","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124307144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1016/j.jat.2013.09.006
S. Stasyuk
{"title":"Best m-term trigonometric approximation of periodic functions of several variables from Nikol'skii-Besov classes for small smoothness","authors":"S. Stasyuk","doi":"10.1016/j.jat.2013.09.006","DOIUrl":"https://doi.org/10.1016/j.jat.2013.09.006","url":null,"abstract":"","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"18 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117420168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1016/j.jat.2020.105521
Antonio J. Durán Guardeño, Mónica Rueda
{"title":"Bispectrality of Meixner type polynomials","authors":"Antonio J. Durán Guardeño, Mónica Rueda","doi":"10.1016/j.jat.2020.105521","DOIUrl":"https://doi.org/10.1016/j.jat.2020.105521","url":null,"abstract":"","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120086435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：