Direct and inverse results in variable Hilbert scales

JOURNAL OF APPROXIMATION THEORY

卷:154

Article

Mathe, Peter¹  Hofmann, Bernd² 

[1] Weierstr Inst Appl Anal & Stochast, D-10117 Berlin, Germany

[2] Tech Univ Chemnitz, Dept Math, D-09107 Chemnitz, Germany

关键词: Variable Hilbert scales;    Source conditions;    Approximability;    Distance functions;    Jackson- and Bernstein-type inequality;    Inverse theorems;    Fenchel duality;   

DOI  :  10.1016/j.jat.2008.01.010

来源: Elsevier

【 摘 要 】

Variable Hilbert scales are ail important tool for the recent analysis of inverse problems ill Hilbert spaces, as these constitute a way to describe smoothness of objects other than functions oil domains. Previous analysis of Such classes of Hilbert spaces focused Oil interpolation properties, which allows Lis to vary between such spaces. In the context of discretization of inverse problems, first results on approxiamation theoretic properties appeared. The present Study is the first which aims at presenting such Spaces ill the context of approximation theory. The authors review and establish direct theorems and also provide inverse theorems, as such are common in approximation theory. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free