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April 2021 Compactness of semigroups of explosive symmetric Markov processes
Kouhei Matsuura
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Kyoto J. Math. 61(1): 97-113 (April 2021). DOI: 10.1215/21562261-2020-0005

Abstract

We investigate spectral properties of explosive symmetric Markov processes. Under a condition on its 1-resolvent, we prove the L1-semigroups of Markov processes become compact operators.

Acknowledgments

The author would like to thank the referees for their valuable comments and suggestions, all of which helped improve the quality of this paper. He would also like to thank Masayoshi Takeda for his helpful comments and encouragement, as well as Kwaśnicki Mateusz, Masanori Hino, and Naotaka Kajino for their helpful comments on Remark 4.3.

Citation

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Kouhei Matsuura. "Compactness of semigroups of explosive symmetric Markov processes." Kyoto J. Math. 61 (1) 97 - 113, April 2021. https://doi.org/10.1215/21562261-2020-0005

Information

Received: 11 December 2018; Revised: 25 January 2019; Accepted: 4 February 2019; Published: April 2021
First available in Project Euclid: 17 December 2020

Digital Object Identifier: 10.1215/21562261-2020-0005

Subjects:
Primary: 60J60
Secondary: 47D07, 47D08

Rights: Copyright © 2021 by Kyoto University

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Vol.61 • No. 1 • April 2021
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