English

Sub-Feller Semigroups Generated by Pseudodifferential Operators on Symmetric Spaces of Noncompact Type

Functional Analysis 2022-08-10 v4

Abstract

We consider global pseudodifferential operators on symmetric spaces of noncompact type, defined using spherical functions. The associated symbols have a natural probabilistic form that extend the notion of the characteristic exponent appearing in Gangolli's L\'evy-Khinchine formula to a function of two variables. The Hille-Yosida-Ray theorem is used to obtain conditions on such a symbol so that the corresponding pseudodifferential operator has an extension that generates a sub-Feller semigroup, generalising existing results for Euclidean space.

Keywords

Cite

@article{arxiv.2107.01817,
  title  = {Sub-Feller Semigroups Generated by Pseudodifferential Operators on Symmetric Spaces of Noncompact Type},
  author = {Rosemary Shewell Brockway},
  journal= {arXiv preprint arXiv:2107.01817},
  year   = {2022}
}