Arkiv för Matematik
Volume 60 (2022)
Beurling’s theorem on the Heisenberg group
Pages: 417 – 442
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