Beurling’s theorem on the Heisenberg group

We formulate and prove an analogue of Beurling’s theorem for the Fourier transform on the Heisenberg group. As a consequence, we deduce Hardy and Cowling–Price theorems.

Keywords

Fourier transform, Beurling’s theorem, Heisenberg group, Hermite and Laguerre functions, Gutzmer’s formula

2010 Mathematics Subject Classification

Primary 42C05, 43A85. Secondary 33C45, 35P10.

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This work was supported by a J. C. Bose Fellowship from the Department of Science and Technology, Government of India.

Received 14 July 2021

Received revised 22 February 2022

Accepted 15 March 2022

Published 26 October 2022