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Transactions of the American Mathematical Society

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Mean value property in limit for eigenfunctions of the Laplace-Beltrami operator


Authors: Muna Naik, Swagato K. Ray and Rudra P. Sarkar
Journal: Trans. Amer. Math. Soc. 373 (2020), 4735-4756
MSC (2010): Primary 43A85; Secondary 22E30
DOI: https://doi.org/10.1090/tran/8078
Published electronically: March 10, 2020
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Abstract: We consider Riemannian symmetric spaces $ X$ of noncompact-type with rank one, which accommodates all hyperbolic spaces. We characterize the eigenfunctions of the Laplace-Beltrami operator on $ X$ with arbitrary complex eigenvalues through an asymptotic version of the ball mean value property as the radius of the ball tends to infinity.


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Additional Information

Muna Naik
Affiliation: Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road, Calcutta 700108, India
Email: mnaik41@gmail.com

Swagato K. Ray
Affiliation: Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road, Calcutta 700108, India
Email: swagato@isical.ac.in

Rudra P. Sarkar
Affiliation: Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road, Calcutta 700108, India
Email: rudra@isical.ac.in

DOI: https://doi.org/10.1090/tran/8078
Keywords: Eigenfunction of Laplacian, Riemannian symmetric spaces, mean value property, hyperbolic spaces
Received by editor(s): April 6, 2018
Received by editor(s) in revised form: August 27, 2019, August 30, 2019, and September 20, 2019
Published electronically: March 10, 2020
Article copyright: © Copyright 2020 American Mathematical Society