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January 2017 Abstract harmonic analysis of wave-packet transforms over locally compact abelian groups
Arash Ghaani Farashahi
Banach J. Math. Anal. 11(1): 50-71 (January 2017). DOI: 10.1215/17358787-3721281

Abstract

This article presents a systematic study for abstract harmonic analysis aspects of wave-packet transforms over locally compact abelian (LCA) groups. Let H be a locally compact group, let K be an LCA group, and let θ:HAut(K) be a continuous homomorphism. We introduce the abstract notion of the wave-packet group generated by θ, and we study basic properties of wave-packet groups. Then we study theoretical aspects of wave-packet transforms. Finally, we will illustrate application of these techniques in the case of some well-known examples.

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Arash Ghaani Farashahi. "Abstract harmonic analysis of wave-packet transforms over locally compact abelian groups." Banach J. Math. Anal. 11 (1) 50 - 71, January 2017. https://doi.org/10.1215/17358787-3721281

Information

Received: 9 November 2015; Accepted: 18 February 2016; Published: January 2017
First available in Project Euclid: 10 November 2016

zbMATH: 1354.43004
MathSciNet: MR3571144
Digital Object Identifier: 10.1215/17358787-3721281

Subjects:
Primary: 43A30
Secondary: 43A15 , 43A25

Keywords: coherent state (covariant) transform , wavelet (Gabor) transform , wave-packet group , wave-packet representation , wave-packet transform

Rights: Copyright © 2017 Tusi Mathematical Research Group

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Vol.11 • No. 1 • January 2017
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