Harmonic functions on semidirect extensions of type nilpotent groups

Author:
Ewa Damek

Journal:
Trans. Amer. Math. Soc. **290** (1985), 375-384

MSC:
Primary 43A80; Secondary 22E27, 22E30, 31C12

DOI:
https://doi.org/10.1090/S0002-9947-1985-0787971-5

MathSciNet review:
787971

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a semidirect extension of a Heisenberg type nilpotent group by the one-parameter group of dilations, equipped with the Riemannian structure, which generalizes this of the symmetric space. Let be a Poisson kernel on with respect to the Laplace-Beltrami operator. Then every bounded harmonic function on is a Poisson integral of a function . Moreover the harmonic measures defined by , are radial and have smooth densities. This seems to be of interest also in the case of a symmetric space of rank .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1985-0787971-5

Keywords:
Laplace-Beltrami operator,
type nilpotent groups

Article copyright:
© Copyright 1985
American Mathematical Society