Ghaani Farashahi, A orcid.org/0000-0003-1580-512X (2017) Abstract harmonic analysis of wave-packet transforms over locally compact abelian groups. Banach Journal of Mathematical Analysis, 11 (1). pp. 50-71. ISSN 1735-8787
Abstract
This article presents a systematic study for abstract harmonic analysis aspects of wave-packet transforms over locally compact abelian (LCA) groups. Let HH be a locally compact group, let KK be an LCA group, and let θ:H→Aut(K)θ:H→Aut(K) be a continuous homomorphism. We introduce the abstract notion of the wave-packet group generated by θθ, 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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Keywords: | coherent state (covariant) transform; wave-packet group; wave-packet representation; wave-packet transform; wavelet (Gabor) transform |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 23 Mar 2020 11:24 |
Last Modified: | 23 Mar 2020 11:24 |
Status: | Published |
Publisher: | Duke University Press |
Identification Number: | 10.1215/17358787-3721281 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:158643 |