The N-widths of spaces of holomorphic functions on bounded symmetric domains. II
type: Item
instance of: scholarly article
title: The N-widths of spaces of holomorphic functions on bounded symmetric domains. II
zbMATH Open document ID: 1006.41014
DOI: 10.1016/S0377-0427(01)00558-1
author: Hongming Ding
published in: Journal of Computational and Applied Mathematics
publication date: 2002-08-22T00:00:00Z
review text: In [J. Approximation Theory 104, No. 1, 121-141 (2000; Zbl 0958.32021)] \textit{K. I. Gross} and \textit{D. St. P. Richards} and the author initiated the study of \(N\)-widths of Hardy-Sobolev and Bergman-Sobolev spaces on bounded symmetric domains of tube type. In this paper, using the structure of Jordan pair, the author extends their results to holomorphic functions spaces on general bounded symmetric domains, of tube type and not of tube type. He studies the weighted Bergman spaces \(A_{\lambda}^2(D)\) and the weighted Bergman-Sobolev space \(A_{2,\lambda, l}(D)\) for \(\lambda\) in the Wallach set \(W\), a nonnegative integer \(l\), and a bounded symmetric domain \(D\). The author obtains exact values of Gel'fand and linear \(N\)-widths of \(A_{2,\lambda, l}(D)\) in the space of continuous functions \(C(\Sigma_{\rho})\), where \(0<\rho<1\), \(\Sigma_{\rho}=\rho\Sigma\), and \(\Sigma\) is the Shilov boundary of \(D\). The Bernstein \(N\)-widths of Hardy-Sobolev space \(H_{\infty,l}(D)\) in the weighted Bergman space \(A^2_{\lambda}(D_{\rho})\) are also given, where \(D_{\rho}=\rho D\).
reviewed by: Saulius Norvidas
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 43A90
zbMATH DE Number: 1787654
zbMATH Keywords: Jordan pair
zbMATH Keywords: bounded symmetric domain
zbMATH Keywords: Shilov boundary
zbMATH Keywords: weighted Bergman space
zbMATH Keywords: Bergman space
zbMATH Keywords: Hardy space
zbMATH Keywords: widths
MaRDI profile type: Publication
cites work: The \(N\)-widths of spaces of holomorphic functions on bounded symmetric domains of tube type
cites work: Function spaces and reproducing kernels on bounded symmetric domains
cites work: The \(N\)-widths of Hardy-Sobolev spaces of several complex variables
cites work: On \(n\)-widths of classes of holomorphic functions with reproducing kernels
cites work: Q3897665
cites work: On \(N\)-widths of holomorphic functions of several variables
cites work: Ismagilov type theorems for linear, Gel'fand and Bernstein \(n\)-widths
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description: scientific article; zbMATH DE number 1787654