On the boundary behaviour of generalized Poisson integrals on symmetric spaces

Schlichtkrull, Henrik

doi:10.1090/S0002-9947-1985-0787965-X

On the boundary behaviour of generalized Poisson integrals on symmetric spaces
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by Henrik Schlichtkrull

Trans. Amer. Math. Soc. 290 (1985), 273-280

DOI: https://doi.org/10.1090/S0002-9947-1985-0787965-X

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Abstract:

On a Riemannian symmetric space $X$ of the noncompact type we introduce a generalized Poisson transformation from functions on the minimal boundary to functions on the maximal compactification whose restrictions to $X$ are eigenfunctions of the invariant differential operators. Some continuity- and "Fatou"-theorems are proved.

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