arXiv subjects

Rosemary Shewell Brockway

Publications and source records attributed to Rosemary Shewell Brockway.

2 recordsLinked to original sources

arXiv2022

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

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 Lévy-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.

math.FA↗

arXiv2019

$L^2$ Properties of Lévy Generators on Compact Riemannian Manifolds

We consider isotropic Lévy processes on a compact Riemannian manifold, obtained from an $\mathbb{R}^d$-valued Lévy process through rolling without slipping. We prove that the Feller semigroups associated with these processes extend to strongly continuous contraction semigroups on $L^p$, for $1\leq p<\infty$, and that they are self-adjoint when $p=2$. When the motion has a non-trivial Brownian part, we prove that the generator has a discrete spectrum of eigenvalues and that the semigroup is trace-class.

math.PR↗