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