Annals of Functional Analysis

A characterisation of the Fourier transform on the‎ ‎Heisenberg group

R‎. ‎Lakshmi Lavanya and S‎. ‎Thangavelu

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Abstract

‎The aim of this paper is to show that any continuous‎ ‎$*$-homomorphism of $L^1(\C^n)$(with twisted convolution as‎ ‎multiplication) into $\CB(L^2(\Rn))$ is essentially a Weyl‎ ‎transform‎. ‎From this we deduce a similar characterisation for the‎ ‎group Fourier transform on the Heisenberg group‎, ‎in terms of‎ ‎convolution‎.

Article information

Source
Ann. Funct. Anal., Volume 3, Number 1 (2012), 109-120.

Dates
First available in Project Euclid: 12 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1399900028

Digital Object Identifier
doi:10.15352/afa/1399900028

Mathematical Reviews number (MathSciNet)
MR2903272

Zentralblatt MATH identifier
1260.43010

Subjects
Primary: 46K05: General theory of topological algebras with involution
Secondary: 42A85‎ ‎43A32

Keywords
Heisenberg group ‎Weyl transform ‎Heisenberg group‎ ‎Fourier transform ‎Hermite functions

Citation

‎Lakshmi Lavanya, R‎.; ‎Thangavelu, S‎. A characterisation of the Fourier transform on the‎ ‎Heisenberg group. Ann. Funct. Anal. 3 (2012), no. 1, 109--120. doi:10.15352/afa/1399900028. https://projecteuclid.org/euclid.afa/1399900028


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References

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