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arXiv · 2107.01817

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

Rosemary Shewell Brockway
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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.

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BibTeXRIS

Rosemary Shewell Brockway. 2021-07-05. Sub-Feller Semigroups Generated by Pseudodifferential Operators on Symmetric Spaces of Noncompact Type. https://arxiv.org/abs/2107.01817

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