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Flat wavelet bases adapted to the homogeneous Sobolev spaces
Author(s) -
Vedel Béatrice
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810725
Subject(s) - sobolev space , mathematics , divergence (linguistics) , homogeneous , wavelet , realization (probability) , pure mathematics , space (punctuation) , mathematical analysis , phenomenon , combinatorics , statistics , artificial intelligence , computer science , physics , quantum mechanics , philosophy , linguistics , operating system
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 case s – n /2 ∉ ℕ since they are also bases of the realization of Ḣ s (ℝ n ). In the critical case s – n /2 ∈ ℕ, they provide a confinement of the divergence in a “small” space. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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