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Two-Level-Split Decomposition of Anisotropic Besov Spaces

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Abstract

Anisotropic Besov spaces (B-spaces) are developed based on anisotropic multilevel ellipsoid covers (dilations) of ℝn. This extends earlier results on anisotropic Besov spaces. Furthermore, sequences of anisotropic bases are constructed and utilized for two-level-split decompositions of the B-spaces and nonlinear m-term approximation.

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Authors and Affiliations

  1. Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056, Aachen, Germany

    Wolfgang Dahmen

  2. 27 Hamaskit St., Herzelia, Israel

    Shai Dekel

  3. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Pencho Petrushev

Authors
  1. Wolfgang Dahmen
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  2. Shai Dekel
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  3. Pencho Petrushev
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Corresponding author

Correspondence to Pencho Petrushev.

Additional information

Communicated by Ronald A. DeVore.

This work has been supported in part by NSF Grant DMS-0709046 and by the Leibniz Program of the German Research Foundation.

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Dahmen, W., Dekel, S. & Petrushev, P. Two-Level-Split Decomposition of Anisotropic Besov Spaces. Constr Approx 31, 149–194 (2010). https://doi.org/10.1007/s00365-009-9058-y

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  • DOI: https://doi.org/10.1007/s00365-009-9058-y

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