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Realizations of homogeneous Sobolev spaces

✍ Scribed by Bourdaud, Gérard

Book ID
121458654
Publisher
Taylor and Francis Group
Year
2011
Tongue
English
Weight
212 KB
Volume
56
Category
Article
ISSN
1747-6933

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## Abstract We discuss the existence and unicity of translation and dilation commuting realizations of the homogeneous spaces \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\dot{B}\_{{p},{q}}^{s}({\mathbb R}^n\!)$\end{document} and \documentclass{article}\usepackage{am

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## Abstract We present a construction of “flat wavelet bases” adapted to the homogeneous Sobolev spaces __Ḣ^s^__ (ℝ^__n__^ ). They solve the problem of the phenomenon of infrared divergence which appears for usual wavelet expansions in __Ḣ^s^__ (ℝ^__n__^ ): these bases remove the divergence in the