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Restricted nonlinear approximation and singular solutions of boundary integral equations

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Analysis in Theory and Applications

Abstract

This paper studies several problems, which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besov spaces B 6r,r (0.1) with 0<σ<∞ and (1+σ)−1<r<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.

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Authors and Affiliations

  1. Mathematisches Institute I Facbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 3, 14195, Berlin, Germany

    Reinhard Hochmuth

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  1. Reinhard Hochmuth
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Correspondence to Reinhard Hochmuth.

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The work of the author has been supported by the Deutsche Forschungsgemeinschaft (DFG) under Grant Ho 1846/1–1.

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Hochmuth, R. Restricted nonlinear approximation and singular solutions of boundary integral equations. Approx. Theory & its Appl. 18, 1–25 (2002). https://doi.org/10.1007/BF02837045

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