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

Naik, Muna; Ray, Swagato; Sarkar, Rudra

doi:10.1090/tran/8078

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

Trans. Amer. Math. Soc. 373 (2020), 4735-4756 Request permission

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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