Direct and inverse results in variable Hilbert scales
type: Item
instance of: scholarly article
title: Direct and inverse results in variable Hilbert scales
zbMATH Open document ID: 1169.41003
author: Peter Mathé
author: Bernd Hofmann
published in: Journal of Approximation Theory
publication date: 2009-02-03T00:00:00Z
review text: Let us consider a non-negative self-adjoint compact and injective operator \(H\) acting in a Hilbert space \(X\). With the help of a singular decomposition of \(H\) and of some set \(\{ \psi \}\) of continuous and strictly convex functions acting from \([0,a]\) in \([0,\infty )\) a scale of Hilbert spaces \(H_\psi ^H\) is introduced. These spaces are studied in the context of approximation theory. Namely, in terms of so-called general sourse conditions, direct and inverse theorems for approximation by a sequence of finite dimensional subspaces of \(X\) are established.
reviewed by: D. K. Ugulava
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 5501948
zbMATH Keywords: variable Hilbert scales
zbMATH Keywords: source conditions
zbMATH Keywords: approximality
zbMATH Keywords: distance functions
zbMATH Keywords: Jackson and Bernstein-type inequality
zbMATH Keywords: inverse theorems
zbMATH Keywords: Fenchel duality
MaRDI profile type: Publication
full work available at URL: j.jat.2008.01.010
OpenAlex ID: W2163898559
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DOI: 10.1016/J.JAT.2008.01.010
description: scientific article; zbMATH DE number 5501948