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 on , is it possible to find a function *F* on such that is continuous for , harmonic for and such that ?

**[1]**Mark Finkelstein and Stephen Scheinberg,*Kernels for solving problems of Dirichlet type in a half-plane*, Advances in Math.**18**(1975), no. 1, 108–113. MR**0382677****[2]**Sigurđur Helgason,*Differential geometry and symmetric spaces*, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR**0145455****[3]**Sigurđur Helgason,*A duality for symmetric spaces with applications to group representations*, Advances in Math.**5**(1970), 1–154 (1970). MR**0263988****[4]**M. Kashiwara, A. Kowata, K. Minemura, K. Okamoto, T. Ōshima, and M. Tanaka,*Eigenfunctions of invariant differential operators on a symmetric space*, Ann. of Math. (2)**107**(1978), no. 1, 1–39. MR**485861**, 10.2307/1971253**[5]**Adam Korányi,*Boundary behavior of Poisson integrals on symmetric spaces*, Trans. Amer. Math. Soc.**140**(1969), 393–409. MR**0245826**, 10.1090/S0002-9947-1969-0245826-X

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1979-0542087-0

Article copyright:
© Copyright 1979
American Mathematical Society