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Strong Equivalences of Approximation Numbers and Tractability of Weighted Anisotropic Sobolev Embeddings

Authors
  • Hao, Jidong1
  • Wang, Heping1
  • 1 Capital Normal University, Beijing, 100048, China , Beijing (China)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Oct 10, 2020
Volume
40
Issue
6
Pages
1765–1782
Identifiers
DOI: 10.1007/s10473-020-0611-x
Source
Springer Nature
Keywords
License
Yellow

Abstract

In this article, we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a = {aj}j≥1 and b = {bj}j≥1 of positive numbers. We obtain strong equivalences of the approximation numbers, and necessary and sufficient conditions on a, b to achieve various notions of tractability of the weighted anisotropic Sobolev embeddings.

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