The N-widths of spaces of holomorphic functions on bounded symmetric domains. II
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 \(D_{\rho}=\rho D\).
scientific article; zbMATH DE number 1787654