Lp-independence of spectral bounds of Feynman–Kac semigroups by continuous additive functionals

We establish conditions for the Lp-independence of spectral bounds of Feynman–Kac semigroup by continuous additive functionals whose Revuz measures are smooth measures of Kato class having non-negative order Green-tightness. Our continuous additive functionals do not necessarily admit bounded variation in general. Examples of Cauchy principal value and Hilbert transform of Brownian local time, and for relativistic symmetric stable processes are presented.