Banach Journal of Mathematical Analysis

Abstract harmonic analysis of wave-packet transforms over locally compact abelian groups

Arash Ghaani Farashahi

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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.

Article information

Banach J. Math. Anal. Volume 11, Number 1 (2017), 50-71.

Received: 9 November 2015
Accepted: 18 February 2016
First available in Project Euclid: 10 November 2016

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Zentralblatt MATH identifier

Primary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
Secondary: 43A25: Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.

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


Ghaani Farashahi, Arash. Abstract harmonic analysis of wave-packet transforms over locally compact abelian groups. Banach J. Math. Anal. 11 (2017), no. 1, 50--71. doi:10.1215/17358787-3721281.

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