Arup Chattopadhyay, Deb Kumar Giri, R. K. Srivastava
Published 2016-07-13Version 1
In this article, we prove that if the group Fourier transform of certain integrable functions on the Heisenberg motion group (or step two nilpotent Lie groups) is of finite rank, then the function is identically zero. These results can be thought as analogous to the Benedicks theorem that dealt with the uniqueness of the Fourier transform of integrable functions on the Euclidean spaces.
Benedicks-Amrein-Berthier theorem for the Heisenberg motion group and quaternion Heisenberg group
Multifunctions determined by integrable functions
Uniqueness of the maximal ideal of operators on the $\ell_p$-sum of $\ell_\infty^n\ (n\in\mathbb{N})$ for $1<p<\infty$
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