On Persson’s Theorem in Local Dirichiet Spaces

Abstract

Given a strongly local, regular and irreducible Dirichlet form $\mathcal{E}$, we prove a version of Persson’s theorem concerning the variational characterization of the bottom of the essential spectrum of the generator $H$ of $\mathcal{E}$. Such a result is then used to prove $L^p$-exponential decay of the "small eigenfunctions" of $H$.