On furstenberg’s characterization of harmonic functions on symmetric spaces
✍ Scribed by Yitzhak Weit
- Publisher
- The Hebrew University Magnes Press
- Year
- 1999
- Tongue
- English
- Weight
- 189 KB
- Volume
- 114
- Category
- Article
- ISSN
- 0021-2172
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📜 SIMILAR VOLUMES
If f # L 1 (d+) is harmonic in the space GÂK, where + is a radial measure with +(GÂK)=1, we have, by the mean value property f = f V +. Conversely, does this mean value property imply that f is harmonic ? In this paper we give a new and natural proof of a result obtained by P. Ahern, A. Flores, W. R
## Abstract New Besov spaces of M‐harmonic functions are introduced on a bounded symmetric domain in ℂ^__n__^. Various characterizations of these spaces are given in terms of the intrinsic metrics, the Laplace‐Beltrami operator and the action of the group of the domain.
Let \(M=G / K\) be a simply connected symmetric space of non-positive curvature. We establish a natural 1-1-correspondence between geodesically convex \(K\)-invariant functions on \(M\) and convex functions, invariant under the Weyl group, on a Cartan subspace.