Stable semigroups on homogeneous trees and hyperbolic spaces. (English) Zbl 1276.60082
Summary: We prove the kernel estimates for subordinated semigroups on homogeneous trees. We study the long-time propagation problem. We exploit this to prove exit-time estimates for large balls in the abstract setting of metric measure spaces. Finally, we give estimates for the Poisson kernel of a ball.
MSC:
| 60J35 | Transition functions, generators and resolvents |
| 47D03 | Groups and semigroups of linear operators |
| 14M17 | Homogeneous spaces and generalizations |
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