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An analogue of Ingham’s theorem on the Heisenberg group

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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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Acknowledgements

The authors are very grateful to the referee for his/her careful reading of the manuscript and offering constructive suggestions. We have incorporated all the corrections and modifications suggested by the referee which have greatly improved the exposition. The work of the first named author is supported by the INSPIRE Faculty Award from the Department of Science and Technology. The second author is supported by Int.Ph.D. scholarship from Indian Institute of Science. The third named author is supported by NBHM Post-Doctoral fellowship from the Department of Atomic Energy (DAE), Government of India. The work of the last named author is supported by J. C. Bose Fellowship from the Department of Science and Technology, Government of India.

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  1. Pritam Ganguly

    Present address: Institut für Mathematik, Universität Paderborn, Warburger Str. 100, 33098, Paderborn, Germany

Authors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Science Education and Research Kolkata, Mohanpur, Nadia, 741246, West Bengal, India

    Sayan Bagchi & Jayanta Sarkar

  2. Department of Mathematics, Indian Institute of Science, Bangalore, 560 012, India

    Pritam Ganguly

  3. Department of Mathematics, Indian Institute of Science, Bangalore, 560 012, India

    Sundaram Thangavelu

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  1. Sayan Bagchi
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Correspondence to Pritam Ganguly.

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Bagchi, S., Ganguly, P., Sarkar, J. et al. An analogue of Ingham’s theorem on the Heisenberg group. Math. Ann. 387, 1073–1104 (2023). https://doi.org/10.1007/s00208-022-02479-5

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