Benedicks-Amrein-Berthier theorem for the Heisenberg motion group and quaternion Heisenberg group

2019/03/29 by Somnath Ghosh, Ghosh, Somnath, R. K. Srivastava +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1904.04023

openalex publication_date 2019/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Since (ℍⁿ\rtimes U(n),U(n)) is a Gelfand pair, an exact analogue of the Heisenberg group result due to Narayanan and Ratnakumar is not possible for the Heisenberg motion group. In this article, we prove that if the Weyl transform of a finitely supported integrable function on the Heisenberg motion group is non-zero only for finitely many Fourier-Wigner pieces and have finite rank, then the function must be zero. We also prove an analogue of the Heisenberg group result on the quaternion Heisenberg group. In the end, a quantitative interpretation of these results is described through strong annihilating pair for the Weyl transform.

Citations

• Heisenberg uniqueness pairs for the Fourier transform on the Heisenberg group

Cited by

• Uncertainty Principles for the Strichartz Fourier transform on the Heisenberg Group

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• Benedick's theorem for the Heisenberg group
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