## Banach Journal of Mathematical Analysis

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

Arash Ghaani Farashahi

#### 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 $\theta:H\to\operatorname{Aut}(K)$ be a continuous homomorphism. We introduce the abstract notion of the wave-packet group generated by $\theta$, 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

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

Dates
Accepted: 18 February 2016
First available in Project Euclid: 10 November 2016

https://projecteuclid.org/euclid.bjma/1478746986

Digital Object Identifier
doi:10.1215/17358787-3721281

Mathematical Reviews number (MathSciNet)
MR3571144

Zentralblatt MATH identifier
1354.43004

#### Citation

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. https://projecteuclid.org/euclid.bjma/1478746986

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