Premium
Wavelet Decompositions of Anisotropic Besov Spaces
Author(s) -
Garrigós Gustavo,
Tabacco Anita
Publication year - 2002
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 - 10.1002/1522-2616(200206)239:1<80::aid-mana80>3.0.co;2-3
Subject(s) - mathematics , wavelet , norm (philosophy) , besov space , pure mathematics , multiresolution analysis , mathematical analysis , characterization (materials science) , dual (grammatical number) , type (biology) , interpolation space , wavelet transform , functional analysis , discrete wavelet transform , artificial intelligence , chemistry , computer science , biochemistry , gene , art , materials science , law , ecology , literature , biology , political science , nanotechnology
In this paper we develop the natural multiresolution analysis framework related to anisotropic Besov spaces B αp , q (ℝ n ). We prove two new Jackson and Bernstein type inequalities for these spaces, and obtain from well‐known techniques [12, 7] new norm equivalences in terms ofweighted sums of the wavelet coefficients. This provides a characterization for B αp , q (ℝ n ) (and for its dual) by means of compactly supported wavelets, which may be applied to the numerical resolution of semi‐elliptic differential equations.