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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Modified Poisson kernels on rank one symmetric spaces


Author: Anna Maria Mantero
Journal: Proc. Amer. Math. Soc. 77 (1979), 211-217
MSC: Primary 22E30; Secondary 31C05, 43A85
MathSciNet review: 542087
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Abstract: An extension is obtained to the case of a real rank one noncompact symmetric space G/K of the solution of the following problem on half-spaces: given an arbitrary continuous function $ f(x)$ on $ {{\mathbf{R}}^n}$, is it possible to find a function F on $ {{\mathbf{R}}^n} \times {{\mathbf{R}}^ + }$ such that $ F(x,y)$ is continuous for $ y > 0$, harmonic for $ y > 0$ and such that $ F(x,0) = f(x)$?


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DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0542087-0
PII: S 0002-9939(1979)0542087-0
Article copyright: © Copyright 1979 American Mathematical Society