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arXiv · 1902.03836

The Positive Maximum Principle on Symmetric Spaces

David Applebaum·Trang Le Ngan
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Abstract

We investigate the Courr\`{e}ge theorem in the context of linear operators $A$ 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.

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David Applebaum, Trang Le Ngan. 2019-02-11. The Positive Maximum Principle on Symmetric Spaces. https://arxiv.org/abs/1902.03836

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