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 R^n, is it possible to find a function F on R^n x R^+ such that F(x, y) is continuous for y > 0, harmonic for y > 0 and such that F(x, 0) = f(x)?
Modified Poisson kernels on rank one symmetric spaces
MANTERO, ANNA MARIA
1979-01-01
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 R^n, is it possible to find a function F on R^n x 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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