Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 11, Number 1 (2017), 50-71.
Abstract harmonic analysis of wave-packet transforms over locally compact abelian groups
This article presents a systematic study for abstract harmonic analysis aspects of wave-packet transforms over locally compact abelian (LCA) groups. Let be a locally compact group, let be an LCA group, and let be a continuous homomorphism. We introduce the abstract notion of the wave-packet group generated by , 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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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.
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