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April 2020 Wavelet frames in $L^2(\mathbb{R}^d)$
Khole Timothy Poumai, Shiv Kumar Kaushik
Rocky Mountain J. Math. 50(2): 677-692 (April 2020). DOI: 10.1216/rmj.2020.50.677

Abstract

We obtain a necessary and sufficient condition for the existence of wavelet frames. We define and study the synthesis and analysis operators associated with wavelet frames. We discuss some applications of operator value (OPV) frames in the theory of wavelet frames. Also, we discuss the minimal property of wavelet frame coefficients and study the property of over completeness of wavelet frames. Various characterizations of wavelet frame, Riesz wavelet basis and orthonormal wavelet basis are given. Further, dual wavelet frames are discussed and a characterization of dual wavelet frames is given. Finally, we give a characterization of a pair of biorthogonal Riesz bases.

Citation

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Khole Timothy Poumai. Shiv Kumar Kaushik. "Wavelet frames in $L^2(\mathbb{R}^d)$." Rocky Mountain J. Math. 50 (2) 677 - 692, April 2020. https://doi.org/10.1216/rmj.2020.50.677

Information

Received: 18 August 2018; Revised: 11 August 2019; Accepted: 30 September 2019; Published: April 2020
First available in Project Euclid: 29 May 2020

zbMATH: 07210989
MathSciNet: MR4104404
Digital Object Identifier: 10.1216/rmj.2020.50.677

Subjects:
Primary: 42C05, 42C15, 42C30, 46B15

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 2 • April 2020
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