Matrix Fourier multipliers for Parseval multi-wavelet frames

    Authors

    Z. Y. Li;D. G. Han

    Comments

    Authors: contact us about adding a copy of your work at [email protected]

    Abbreviated Journal Title

    Appl. Comput. Harmon. Anal.

    Keywords

    Wavelets; Frames; Multi-wavelet frames; Fourier multipliers; Matrix; Fourier multipliers; CONNECTIVITY; L-2(R-D); DENSITY; SET; Mathematics, Applied; Physics, Mathematical

    Abstract

    A Fourier multiplier for orthonormal wavelets is an L-infinity-function that sends every orthonormal wavelet to an orthonormal wavelet. This type of multipliers plays an important role in the study of basic properties of wavelets including some geometrical and topological properties of the wavelet theory. Matrix Fourier multipliers are matrices with L-infinity-function entries that map Parseval multi-wavelet frames to Parseval multi-wavelet frames. Like Fourier wavelet multiplier, matrix Fourier multipliers can be used to derive new multi-wavelet frames and can help us better understand the basic theory of multi-wavelet frame theory. In this paper we characterize all the matrix Fourier multipliers for Parseval multi-wavelet frames. (C) 2012 Elsevier Inc. All rights reserved.

    Journal Title

    Applied and Computational Harmonic Analysis

    Volume

    35

    Issue/Number

    3

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    407

    Last Page

    418

    WOS Identifier

    WOS:000324848400003

    ISSN

    1063-5203

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