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J. Approx. Theory最新文献

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Lp Markov-Bernstein Inequalities on Arcs of the Circle 圆弧上的Lp Markov-Bernstein不等式
J. Approx. Theory Pub Date : 1900-01-01 DOI: 10.1006/jath.2000.3502
D. Lubinsky
{"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}
引用次数: 12
On the Construction and Frequency Localization of Finite Orthogonal Quadrature Filters 有限正交正交滤波器的构造与频率定位
J. Approx. Theory Pub Date : 1900-01-01 DOI: 10.1006/jath.2000.3514
M. Nielsen
{"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}
引用次数: 54
On Exact Values of n-Widths in a Hilbert Space 希尔伯特空间n-宽度的精确值
J. Approx. Theory Pub Date : 1900-01-01 DOI: 10.1006/jath.2000.3497
G. Magaril-Il'yaev, K. Osipenko, V. Tikhomirov
{"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}
引用次数: 5
A Trigonometric Quadrature Rule for Cauchy Integrals with Jacobi Weight 具有Jacobi权值的Cauchy积分的三角求积规则
J. Approx. Theory Pub Date : 1900-01-01 DOI: 10.1006/jath.2000.3513
Philsu Kim
{"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}
引用次数: 4
Best m-term trigonometric approximation of periodic functions of several variables from Nikol'skii-Besov classes for small smoothness 小平滑Nikol'skii-Besov类中若干变量周期函数的最佳m项三角逼近
J. Approx. Theory Pub Date : 1900-01-01 DOI: 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}
引用次数: 10
Bispectrality of Meixner type polynomials Meixner型多项式的双谱性
J. Approx. Theory Pub Date : 1900-01-01 DOI: 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}
引用次数: 2
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