Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (6): 1765-1782.doi: 10.1007/s10473-020-0611-x

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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).

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

CLC Number: 

  • 41A25
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