Mean value property in limit for eigenfunctions of the Laplace–Beltrami operator
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- by Muna Naik, Swagato K. Ray and Rudra P. Sarkar PDF
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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.References
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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
- MR Author ID: 641235
- Email: swagato@isical.ac.in
- Rudra P. Sarkar
- Affiliation: Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road, Calcutta 700108, India
- MR Author ID: 618544
- Email: rudra@isical.ac.in
- 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
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 4735-4756
- MSC (2010): Primary 43A85; Secondary 22E30
- DOI: https://doi.org/10.1090/tran/8078
- MathSciNet review: 4127861