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2012 A characterisation of the Fourier transform on the‎ ‎Heisenberg group
R‎. ‎Lakshmi Lavanya, S‎. ‎Thangavelu
Ann. Funct. Anal. 3(1): 109-120 (2012). DOI: 10.15352/afa/1399900028


‎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.


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R‎. ‎Lakshmi Lavanya. S‎. ‎Thangavelu. "A characterisation of the Fourier transform on the‎ ‎Heisenberg group." Ann. Funct. Anal. 3 (1) 109 - 120, 2012.


Published: 2012
First available in Project Euclid: 12 May 2014

zbMATH: 1260.43010
MathSciNet: MR2903272
Digital Object Identifier: 10.15352/afa/1399900028

Primary: 46K05
Secondary: 42A85‎ , ‎43A32

Keywords: Heisenberg group , ‎Heisenberg group‎ ‎Fourier transform , ‎Hermite functions , ‎Weyl transform

Rights: Copyright © 2012 Tusi Mathematical Research Group

Vol.3 • No. 1 • 2012
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