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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the boundary behaviour of generalized Poisson integrals on symmetric spaces


Author: Henrik Schlichtkrull
Journal: Trans. Amer. Math. Soc. 290 (1985), 273-280
MSC: Primary 43A85; Secondary 22E30, 53C35
MathSciNet review: 787965
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0787965-X
PII: S 0002-9947(1985)0787965-X
Keywords: Poisson integral, symmetric space, compactification, boundary, Fatou theorem
Article copyright: © Copyright 1985 American Mathematical Society