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Constructive Approximation

, Volume 14, Issue 1, pp 1–26 | Cite as

Hyperbolic Wavelet Approximation

  • R. A. DeVore
  • S. V. Konyagin
  • V. N. Temlyakov
Article

Abstract.

We study the multivariate approximation by certain partial sums (hyperbolic wavelet sums) of wavelet bases formed by tensor products of univariate wavelets. We characterize spaces of functions which have a prescribed approximation error by hyperbolic wavelet sums in terms of a K -functional and interpolation spaces. The results parallel those for hyperbolic trigonometric cross approximation of periodic functions [DPT].

Key words. Hyperbolic wavelets,Multivariate wavelets,Interpolation spaces. .AMS Classification.  41A63 46C99. <lsiheader> <onlinepub>8 May,1998  <editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;R.A. DeVore E.B.Saff&lsilt;/a&lsigt; <pdfname>14n1p1. pdf <pdfexist>yes <htmlexist>no <htmlfexist>no <texexist>yes <sectionname> </lsiheader> 

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Copyright information

© Springer-Verlag New York 1997

Authors and Affiliations

  • R. A. DeVore
    • 1
  • S. V. Konyagin
    • 2
  • V. N. Temlyakov
    • 3
  1. 1.Department of Mathematics University of South Carolina Columbia SC 29208 USAUS
  2. 2.Department OPU, Mech.-Math. Moscow State University Leninskie Gory Moscow 117234 RussiaRU
  3. 3.Department of Mathematics University of South Carolina Columbia SC 29208 USAUS

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