数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (6): 1765-1782.doi: 10.1007/s10473-020-0611-x

• 论文 • 上一篇    下一篇

STRONG EQUIVALENCES OF APPROXIMATION NUMBERS AND TRACTABILITY OF WEIGHTED ANISOTROPIC SOBOLEV EMBEDDINGS

郝季东, 汪和平   

  1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • 收稿日期:2019-07-08 修回日期:2020-07-17 出版日期:2020-12-25 发布日期:2020-12-30
  • 通讯作者: Heping WANG,E-mail:wanghp@cnu.edu.cn E-mail:wanghp@cnu.edu.cn
  • 作者简介:Jidong HAO,E-mail:1047695025@qq.com
  • 基金资助:
    Supported by the National Natural Science Foundation of China (11671271) and the Natural Science Foundation of Beijing Municipality (1172004).

STRONG EQUIVALENCES OF APPROXIMATION NUMBERS AND TRACTABILITY OF WEIGHTED ANISOTROPIC SOBOLEV EMBEDDINGS

Jidong HAO, Heping WANG   

  1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • Received:2019-07-08 Revised:2020-07-17 Online:2020-12-25 Published:2020-12-30
  • Contact: Heping WANG,E-mail:wanghp@cnu.edu.cn E-mail:wanghp@cnu.edu.cn
  • Supported by:
    Supported by the National Natural Science Foundation of China (11671271) and the Natural Science Foundation of Beijing Municipality (1172004).

摘要: In this article, we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a=$\{a_j\}_{j\geq1}$ and b=$\{b_j\}_{j\geq1}$ 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.

关键词: strong equivalences, tractability, approximation numbers, weighted anisotropic spaces, analytic Korobov spaces

Abstract: In this article, we study multivariate approximation defined over weighted anisotropic Sobolev spaces which depend on two sequences a=$\{a_j\}_{j\geq1}$ and b=$\{b_j\}_{j\geq1}$ 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.

Key words: strong equivalences, tractability, approximation numbers, weighted anisotropic spaces, analytic Korobov spaces

中图分类号: 

  • 41A25