The Positive Maximum Principle on Symmetric Spaces
Functional Analysis
2019-03-06 v2
Abstract
We investigate the Courr\`{e}ge theorem in the context of linear operators that satisfy the positive maximum principle on a space of continuous functions over a symmetric space. Applications are given to Feller--Markov processes. We also introduce Gangolli operators, which satisfy the positive maximum principle, and generalise the form associated with the generator of a L\'{e}vy process on a symmetric space. When the space is compact, we show that Gangolli operators are pseudo--differential operators having scalar symbols.
Keywords
Cite
@article{arxiv.1902.03836,
title = {The Positive Maximum Principle on Symmetric Spaces},
author = {David Applebaum and Trang Le Ngan},
journal= {arXiv preprint arXiv:1902.03836},
year = {2019}
}