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N-term approximation in anisotropic function spaces

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OriginalspracheEnglisch
Seiten (von - bis)131-149
Seitenumfang19
FachzeitschriftMathematische Nachrichten
Jahrgang244
PublikationsstatusVeröffentlicht - 2002
Extern publiziertJa

Abstract

In L2((0, 1)2) infinitely many different biorthogonal wavelet bases may be introduced by taking tensor products of one-dimensional biorthogonal wavelet bases on the interval (0, 1). Most well-known are the standard tensor product bases and the hyperbolic bases. In [23, 24] further biorthogonal wavelet bases are introduced, which provide wavelet characterizations for functions in anisotropic Besov spaces. Here we address the following question: Which of those biorthogonal tensor product wavelet bases is the most appropriate one for approximating nonlinearly functions from anisotropic Besov spaces? It turns out, that the hyperbolic bases lead to nonlinear algorithms which converge as fast as the corresponding schemes with respect to specific anisotropy adapted bases.

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N-term approximation in anisotropic function spaces. / Hochmuth, Reinhard.
in: Mathematische Nachrichten, Jahrgang 244, 2002, S. 131-149.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Hochmuth R. N-term approximation in anisotropic function spaces. Mathematische Nachrichten. 2002;244:131-149. doi: 10.1002/1522-2616(200210)244:1<131::AID-MANA131>3.0.CO;2-G
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