The Positive Maximum Principle on Lie Groups
Functional Analysis
2019-07-31 v6
Abstract
We extend a classical theorem of Courr\`{e}ge to Lie groups in a global setting, thus characterising all linear operators on the space of smooth functions of compact support that satisfy the positive maximum principle. We show that these are L\'{e}vy type operators (with variable characteristics), and pseudo--differential operators when the group is compact. If the characteristics are constant, then the operator is the generator of the contraction semigroup associated to a convolution semigroup of sub--probability measures.
Keywords
Cite
@article{arxiv.1809.04947,
title = {The Positive Maximum Principle on Lie Groups},
author = {David Applebaum and Trang Le Ngan},
journal= {arXiv preprint arXiv:1809.04947},
year = {2019}
}