Benedicks’ theorem for the Heisenberg group

Narayanan, E. K.; Ratnakumar, P.

doi:10.1090/S0002-9939-10-10272-X

Benedicks’ theorem for the Heisenberg group
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by E. K. Narayanan and P. K. Ratnakumar PDF

Proc. Amer. Math. Soc. 138 (2010), 2135-2140 Request permission

Abstract:

If an integrable function $f$ on the Heisenberg group is supported on the set $B \times \mathbb {R}$ where $B \subset \mathbb {C}^n$ is compact and the group Fourier transform $\hat {f}(\lambda )$ is a finite rank operator for all $\lambda \in \mathbb {R} \setminus \{0\},$ then $f \equiv 0.$

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