Compactness of semigroups of explosive symmetric Markov processes

TL;DR

This paper studies the spectral properties of explosive symmetric Markov processes and proves that under certain lifetime conditions, their associated $L^1$-semigroups are compact operators.

Contribution

It establishes the compactness of $L^1$-semigroups for explosive symmetric Markov processes under specific lifetime conditions, advancing spectral analysis in this area.

Findings

$L^1$-semigroups become compact under lifetime conditions

Spectral properties of explosive symmetric Markov processes are characterized

Provides conditions for semigroup compactness in explosive cases

Abstract

In this paper, we investigate spectral properties of explosive symmetric Markov processes. Under a condition on its life time, we prove the $L^1$-semigroup of Markov processes become compact operators.