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On Parseval Wavelet Frames via Multiresolution Analyses in $H_{G}^{2}$

Part of: Nontrigonometric harmonic analysis

Published online by Cambridge University Press:  06 December 2019

A. San Antolín
A. San Antolín*
Affiliation:
Departamento de Matemáticas, Universidad de Alicante, 03080 Alicante, Spain Email: angel.sanantolin@ua.es
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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.

Keywords

dilation matrixextension principleFourier transformrefinable functiontight wavelet frame

MSC classification

Primary: 42C40: Wavelets and other special systems
Secondary: 42C15: General harmonic expansions, frames
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 1 , March 2020 , pp. 157 - 172
Copyright
© Canadian Mathematical Society 2019

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