On Parseval Wavelet Frames via Multiresolution Analyses in

Abstract We give a characterization of all Parseval wavelet frames arising from a given frame multiresolution analysis. As a consequence, we obtain a description of all Parseval wavelet frames associated with a frame multiresolution analysis. These results are based on a version of Oblique Extension...

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Bibliographic Details
Published inCanadian mathematical bulletin Vol. 63; no. 1; pp. 157 - 172
Main Author San Antolín, A.
Format Journal Article
LanguageEnglish
Published Montreal Cambridge University Press 01.03.2020
Subjects
Fourier transforms
Frames
Mathematics
Matrix
Multiresolution analysis
Subspaces
Wavelet analysis
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Summary:Abstract We give a characterization of all Parseval wavelet frames arising from a given frame multiresolution analysis. As a consequence, we obtain a description of all Parseval wavelet frames associated with a frame multiresolution analysis. These results are based on a version of Oblique Extension Principle with the assumption that the origin is a point of approximate continuity of the Fourier transform of the involved refinable functions. Our results are written for reducing subspaces.
ISSN:0008-4395
1496-4287
DOI:10.4153/S0008439519000341