Quasi-biorthogonal frame multiresolution analyses and wavelets

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We introduce the concepts of quasi-biorthogonal frame multiresolution analyses and quasi-biorthogonal frame wavelets which are natural generalizations of biorthogonal multiresolution analyses and biorthogonal wavelets, respectively. Necessary and sufficient conditions for quasi-biorthogonal frame multiresolution analyses to admit quasi-biorthogonal wavelet frames are given, and a non-trivial example of quasi-biorthogonal frame multiresolution analyses admitting quasi-biorthogonal frame wavelets is constructed. Finally, we characterize the pair of quasi-biorthogonal frame wavelets that is associated with quasi-biorthogonal frame multiresolution analyses.
Publisher
SPRINGER
Issue Date
2003-02
Language
English
Article Type
Article
Keywords

SHIFT-INVARIANT SUBSPACES; BASES; DECOMPOSITIONS; L(2)(R(D)); SPACES

Citation

ADVANCES IN COMPUTATIONAL MATHEMATICS, v.18, no.2-4, pp.269 - 296

ISSN
1019-7168
DOI
10.1023/A:1021371227388
URI
http://hdl.handle.net/10203/80736
Appears in Collection
MA-Journal Papers(저널논문)
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