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2014 Revisiting the Fourier transform on the Heisenberg group
R. Lakshmi Lavanya, S. Thangavelu
Publ. Mat. 58(1): 47-63 (2014).


A recent theorem of S. Alesker, S. Artstein-Avidan and V. Milman characterises the Fourier transform on $ {\mathbb R}^{n} $ as essentially the only transform on the space of tempered distributions which interchanges convolutions and pointwise products. In this note we study the image of the Schwartz space on the Heisenberg group under the Fourier transform and obtain a similar characterisation for the Fourier transform on the Heisenberg group


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R. Lakshmi Lavanya. S. Thangavelu. "Revisiting the Fourier transform on the Heisenberg group." Publ. Mat. 58 (1) 47 - 63, 2014.


Published: 2014
First available in Project Euclid: 20 December 2013

zbMATH: 1285.43003
MathSciNet: MR3161508

Primary: 35K08 , 43A30 , 43A70

Keywords: Fourier transform , Fourier-Weyl transform , heat kernel , Heisenberg group , Schwartz class

Rights: Copyright © 2014 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.58 • No. 1 • 2014
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