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Asymptotic mean value property for eigenfunctions of the Laplace–Beltrami operator on Damek–Ricci spaces

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Abstract

Let S be a Damek–Ricci space equipped with the Laplace–Beltrami operator \(\Delta \). In this paper, we characterize all eigenfunctions of \(\Delta \) through sphere, ball and shell averages as the radius (of sphere, ball or shell) tends to infinity.

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Acknowledgements

We are thankful to an unknown referee whose suggestions and criticism helped us to improve an earlier draft of this paper.

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Authors and Affiliations

  1. Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Prayagraj, 211 019, India

    Muna Naik

  2. Stat-Math Unit, Indian Statistical Institute, 203 B. T. Rd., Calcutta, 700108, India

    Rudra P. Sarkar

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  1. Muna Naik
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  2. Rudra P. Sarkar
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Correspondence to Muna Naik.

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Muna Naik is supported by INSPIRE faculty fellowship from the Department of Science and Technology, Government of India (DST/INSPIRE/04/2020/001193, IFA20-MA-151).

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Naik, M., Sarkar, R.P. Asymptotic mean value property for eigenfunctions of the Laplace–Beltrami operator on Damek–Ricci spaces. Annali di Matematica 201, 1583–1605 (2022). https://doi.org/10.1007/s10231-021-01172-9

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  • DOI: https://doi.org/10.1007/s10231-021-01172-9

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