"On the pointwise converse of Fatou’s theorem for Euclidean and real hy" by Jayanta Sarkar
 

On the pointwise converse of Fatou’s theorem for Euclidean and real hyperbolic spaces

Article Type

Research Article

Publication Title

Israel Journal of Mathematics

Abstract

In this article, we extend a result of L. Loomis and W. Rudin, regarding boundary behavior of positive harmonic functions on the upper half space ℝ+n+1. We show that similar results remain valid for more general approximate identities. We apply this result to prove a result regarding boundary behavior of certain nonnegative eigenfunctions of the Laplace-Beltrami operator on real hyperbolic space ℍn. We shall also prove a generalization of a result regarding large time behavior of a solution of the heat equation proved in [17]. We use this result to prove a result regarding asymptotic behavior of certain eigenfunctions of the Laplace-Beltrami operator on real hyperbolic space ℍn.

First Page

179

Last Page

209

DOI

10.1007/s11856-022-2336-0

Publication Date

10-1-2022

Comments

Open Access, Green

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