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

 

Fine convergence and admissible convergence for symmetric spaces of rank one


Authors: Adam Korányi and J. C. Taylor
Journal: Trans. Amer. Math. Soc. 263 (1981), 169-181
MSC: Primary 32M15; Secondary 31C05, 43A85
MathSciNet review: 590418
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Abstract: The connections between fine convergence in the sense of potential theory and admissible convergence to the boundary for quotients of eigenfunctions of the Laplace-Beltrami operator are investigated. This leads to a version of the local Fatou theorem on symmetric spaces of rank one which is considerably stronger than previously known results.

The appendix establishes the relationship between harmonic measures on the intersection of the Martin boundaries of a domain and a subdomain.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0590418-1
PII: S 0002-9947(1981)0590418-1
Keywords: Rank one symmetric space, admissible convergence, eigenfunction of Laplace-Beltrami operator, fine convergence, Martin boundary, local Fatou theorem
Article copyright: © Copyright 1981 American Mathematical Society