An analogue of Ingham's theorem on the Heisenberg group

2022/04/21 by Sayan Bagchi, Bagchi, Sayan, Pritam Ganguly +5
Mathematics · Physics and Astronomy · #26E10 #33C45 #46E35 #Advanced Differential Geometry Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Primary: 43A80. Secondary: 22E25

paper · pdf · doi:10.48550/arxiv.2204.10017

openalex publication_date 2022/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an exact analogue of Ingham's uncertainty principle for the group Fourier transform on the Heisenberg group. This is accomplished by explicitly constructing compactly supported functions on the Heisenberg group whose operator-valued Fourier transforms have suitable Ingham type decay and proving an analogue of Chernoff's theorem for the family of special Hermite operators.

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