Jackson inequality in \(L_{2}(\mathbb T^{N})\) with generalized modulus of continuity
type: Item
instance of: scholarly article
title: Jackson inequality in \(L_{2}(\mathbb T^{N})\) with generalized modulus of continuity
zbMATH Open document ID: 1229.41012
DOI: 10.1134/S0081543809060170
author: S. N. Vasil'ev
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2011-11-02T00:00:00Z
review text: After a special modulus of continuity is defined via a sequence of coefficients which are absolutely summable and sum to zero, approximation estimates are considered. Specifically, the error of approximation of \(2\pi\)-periodic, multivariate, square-integrable functions by approximants from linear combinations of exponentials whose complex powers are from a prescribed, fixed set is bounded above. These powers have to be multi-integer valued, so in particular the exponentials are also \(2\pi\)-periodic. In this set-up a Jackson-type error estimate is established.
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A45
zbMATH DE Number: 5966569
zbMATH Keywords: Jackson inequality
zbMATH Keywords: generalized modulus of continuity
zbMATH Keywords: multidimensional approximation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5966569