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

2021/07/05 by Rosemary Shewell Brockway, Brockway, Rosemary Shewell
Economics, Econometrics and Finance · Mathematics · #43A85 #47D07 #47G20 #47G30 #60B15 #60G53 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2107.01817

openalex publication_date 2021/07/05 · openalex created_date 2023/02/13 · openalex updated_date 2026/07/28

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 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.

Related

• Non-Archimedean pseudodifferential operators and Feller Semigroups
• Pseudodifferential operators of mixed type adapted to distributions of k-planes
• Patterson-Sullivan distributions for symmetric spaces of the noncompact type
• Pseudodifferential operators associated with a semigroup of operators
• Feller Semigroups Obtained by Variable Order Subordination