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

 

Fatou theorems for eigenfunctions of the invariant differential operators on symmetric spaces


Author: H. Lee Michelson
Journal: Trans. Amer. Math. Soc. 177 (1973), 257-274
MSC: Primary 53C35; Secondary 43A85
MathSciNet review: 0319113
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Abstract: On a Riemannian symmetric space of noncompact type we introduce a generalization of the Poisson kernel which may be used to generate simultaneous eigenfunctions of the invariant differential operators with eigenvalues not necessarily zero. We investigate the boundary behavior of our generalized Poisson integrals, extending to them many of the Fatou-type theorems known for harmonic functions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0319113-6
PII: S 0002-9947(1973)0319113-6
Keywords: Generalized Poisson integrals, unrestricted admissible convergence, products of rank-one spaces, restricted admissible convergence
Article copyright: © Copyright 1973 American Mathematical Society