Acta Mathematica Sinica

, Volume 22, Issue 6, pp 1667–1678

N–Widths and Average Widths of Besov Classes in Sobolev Spaces

  • Gui Qiao Xu* **
  • Yong Sheng Sun*
  • Yong Ping Liu* **
ORIGINAL ARTICLES

DOI: 10.1007/s10114-005-0692-4

Cite this article as:
Xu* **, G.Q., Sun*, Y.S. & Liu* **, Y.P. Acta Math Sinica (2006) 22: 1667. doi:10.1007/s10114-005-0692-4

Abstract

In this paper, we consider the n–widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov n–widths, the linear n–widths, the Gel’fand n–widths, in the Sobolev spaces on Td, and the infinite–dimensional widths and the average widths in the Sobolev spaces on Rd are obtained, respectively.

Keywords

Besov classn–widthSobolev spaceAverage width

MR (2000) Subject Classification

41A4646E35

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gui Qiao Xu* **
    • 1
    • 2
  • Yong Sheng Sun*
    • 3
  • Yong Ping Liu* **
    • 3
  1. 1.School of Mathematical SciencesBeijing Normal UniversityBeijing 100875P. R. China
  2. 2.School of Mathematical SciencesTianjin Normal UniversityTianjin 300074P. R. China
  3. 3.School of Mathematical SciencesBeijing Normal UniversityBeijing 100875P. R. China