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Revisiting the Fourier transform on the Heisenberg group

R. Lakshmi Lavanya and S. Thangavelu

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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

Article information

Publ. Mat., Volume 58, Number 1 (2014), 47-63.

First available in Project Euclid: 20 December 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 43A70: Analysis on specific locally compact and other abelian groups [See also 11R56, 22B05] 35K08: Heat kernel

Heisenberg group Fourier transform Fourier-Weyl transform Schwartz class heat kernel


Lavanya, R. Lakshmi; Thangavelu, S. Revisiting the Fourier transform on the Heisenberg group. Publ. Mat. 58 (2014), no. 1, 47--63.

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