$L^p$-independence of spectral bounds of generalized non-local Feynman-Kac semigroups

TL;DR

This paper establishes criteria under which the spectral bounds of generalized non-local Feynman-Kac semigroups remain consistent across different L^p spaces for symmetric Markov processes, extending understanding of spectral properties.

Contribution

It introduces new criteria for L^p-independence of spectral bounds in non-local Feynman-Kac semigroups involving additive functionals with zero quadratic variation.

Findings

Criteria for L^p-independence of spectral bounds established

Applicable to processes with both continuous and discontinuous additive functionals

Enhances understanding of spectral stability in non-local semigroups

Abstract

Let $X$ be a symmetric strong Markov process on a Luzin space. In this paper, we present criteria of the $L^p$-independence of spectral bounds for generalized non-local Feynman-Kac semigroups of $X$ that involve continuous additive functionals of $X$ having zero quadratic variations and discontinuous additive functionals of $X$.