Uniqueness of the group Fourier transform on certain nilpotent Lie groups
Functional Analysis
2018-02-26 v6
Abstract
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 an analogue to the Benedicks theorem that dealt with the uniqueness of the Fourier transform of integrable functions on the Euclidean spaces.
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Cite
@article{arxiv.1607.03832,
title = {Uniqueness of the group Fourier transform on certain nilpotent Lie groups},
author = {A. Chattopadhyay and D. K. Giri and R. K. Srivastava},
journal= {arXiv preprint arXiv:1607.03832},
year = {2018}
}
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