Square-integrability of multivariate metaplectic wave-packet representations

Abstract

This paper presents a systematic study for harmonic analysis of metaplectic wave-packet representations on the Hilbert function space L2(Rd). The abstract notions of symplectic wave-packet groups and metaplectic wave-packet representations will be introduced. We then present an admissibility condition on closed subgroups of the real symplectic group Sp(Rd), which guarantees the square-integrability of the associated metaplectic wave-packet representation on L2(Rd).

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Authors/Creators:	Ghaani Farashahi, A https://orcid.org/0000-0003-1580-512X
Copyright, Publisher and Additional Information:	© 2017 IOP Publishing Ltd. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. To view a copy of this license, visit https://creativecommons.org/licenses/by/3.0/.
Keywords:	Symplectic group, multivariate metaplectic wave-packet representations, symplectic wave-packet group, metaplectic wave-packet transform, square-integrable representations
Dates:	Accepted: 25 January 2017 Published (online): 31 January 2017 Published: 17 March 2017
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:	03 Mar 2020 14:30
Last Modified:	22 Jun 2020 14:42
Status:	Published
Publisher:	Institute of Physics Publishing
Identification Number:	https://doi.org/10.1088/1751-8121/aa5c08

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Square-integrability of multivariate metaplectic wave-packet representations

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