Bulletin of the Belgian Mathematical Society - Simon Stevin

Continuous Gabor transform for a class of non-Abelian groups

Arash Ghaani Farashahi and Rajabali Kamyabi-Gol

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Abstract

In this article we define the continuous Gabor transform for second countable, non-abelian, unimodular and type I groups and also we investigate a Plancherel formula and an inversion formula for our definition. As an example we show that how these formulas work for the Heisenberg group and also the matrix group ${SL(2,\mathbb{R})}$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 4 (2012), 683-701.

Dates
First available in Project Euclid: 23 November 2012

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1353695909

Digital Object Identifier
doi:10.36045/bbms/1353695909

Mathematical Reviews number (MathSciNet)
MR3009030

Zentralblatt MATH identifier
1268.43002

Subjects
Primary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 43A32: Other transforms and operators of Fourier type 43A65: Representations of groups, semigroups, etc. [See also 22A10, 22A20, 22Dxx, 22E45] 22D10: Unitary representations of locally compact groups

Keywords
continuous Gabor transform Fourier transform Plancherel formula Plancherel measure continuous unitary representation primary representation type I group unimodular group

Citation

Farashahi, Arash Ghaani; Kamyabi-Gol, Rajabali. Continuous Gabor transform for a class of non-Abelian groups. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 4, 683--701. doi:10.36045/bbms/1353695909. https://projecteuclid.org/euclid.bbms/1353695909


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