Ghaani Farashahi, A orcid.org/0000-0003-1580-512X (2017) Operator-Valued Continuous Gabor Transforms over Non-unimodular Locally Compact Groups. Mediterranean Journal of Mathematics, 14 (3). 136. ISSN 1660-5446
Abstract
In this article, we present the abstract harmonic analysis aspects of the operator-valued continuous Gabor transform (CGT) on second countable, non-unimodular, and type I locally compact groups. We show that the operator-valued continuous Gabor transform CGT satisfies a Plancherel formula and an inversion formula. As an example, we study these results on the continuous affine group.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
Keywords: | Continuous Gabor transform, Fourier transform, Plancherel formula, Plancherel measure, unitary representation, irreducible representation, primary representation, type I group, non-unimodular group, measurable field of operators |
Dates: |
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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 13:41 |
Last Modified: | 23 Mar 2020 13:41 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s00009-017-0936-4 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:158637 |
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