Applebaum, D. and Le Ngan, T. (2020) The positive maximum principle on symmetric spaces. Positivity, 24 (5). pp. 1519-1533. ISSN 1385-1292
Abstract
We investigate the Courrège 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 Lévy process on a symmetric space. When the space is compact, we show that Gangolli operators are pseudo-differential operators having scalar symbols.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2020. Open Access: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Positive maximum principle; Courrege theorem, symmetric space; Lie group; Lie algebra; Levy kernel; Feller process; Spherical Levy process; Pseudo-differential operator |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 17 Mar 2020 15:41 |
Last Modified: | 06 Dec 2021 18:40 |
Status: | Published |
Publisher: | Springer Science and Business Media LLC |
Refereed: | Yes |
Identification Number: | 10.1007/s11117-020-00746-w |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:158361 |
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