Arkiv för Matematik

Volume 60 (2022)

Number 2

Beurling’s theorem on the Heisenberg group

Pages: 417 – 442



Sundaram Thangavelu (Department of Mathematics, Indian Institute of Science, Bangalore, India)


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.


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

2010 Mathematics Subject Classification

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

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