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Analogues of theorems of Chernoff and Ingham on the Heisenberg group

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Abstract

We prove an analogue of Chernoff’s theorem for the Laplacian Δℍ on the Heisenberg group ℍn. As an application, we prove Ingham type theorems for the group Fourier transform on ℍn and also for the spectral projections associated to the sublaplacian.

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Acknowledgments

The first author is supported by an Int. Ph.D. scholarship from the Indian Institute of Science. The second author is supported by a J. C. Bose Fellowship from the Department of Science and Technology, Government of India.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Science, 560012, Bangalore, India

    Pritam Ganguly & Sundaram Thangavelu

Authors
  1. Pritam Ganguly
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  2. Sundaram Thangavelu
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Correspondence to Pritam Ganguly.

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Note added in the proof

The proof of Theorem 1.4 presented in [1] is not complete. As a consequence, the converse part of Theorem 1.6 remains unproved. For the correct version we refer the reader to [1].

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Ganguly, P., Thangavelu, S. Analogues of theorems of Chernoff and Ingham on the Heisenberg group. JAMA 149, 281–305 (2023). https://doi.org/10.1007/s11854-022-0252-1

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  • DOI: https://doi.org/10.1007/s11854-022-0252-1

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