Research ArticleNo Access

Wavelet frame operators and admissible frames

T. C. Easwaran Nambudiri

https://orcid.org/0000-0002-3677-0918

Department of Mathematics, Government Brennen College, Dharmadam, Thalassery, Kerala 670106, India

E-mail Address: easwarantc@gmail.com

Corresponding author.

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and

K. Parthasarathy

Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, India

E-mail Address: krishnanp.sarathy@gmail.com

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https://doi.org/10.1142/S1793557121501606Cited by:0 (Source: Crossref)

Abstract

Whereas a characterization of Weyl–Heisenberg frame operators is known, the important class of wavelet frame operators is yet to be characterized. We fill this lacuna in this paper. We first look at the problem in an abstract setting, by looking at a special class of Hilbert frames which we call admissible frames. A simple characterization of frame operators of this class of frames is obtained in terms of “local commutativity” of operators and, specializing to wavelet frames, this leads to a characterization of wavelet frame operators on $L^{2} (ℝ)$ . Necessary and sufficient conditions for two admissible frames to be dual to each other are also presented.

Communicated by O. Christensen

Keywords:

AMSC: 42C15

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