Criticality and subcriticality of generalized Schrödinger forms

Abstract

Let $\mathcal{E}$ be a Dirichlet form and $\mu$ a positive Kato measure. We define criticality and subcriticality for the Schrödinger form, $\mathcal{E}(\cdot,\cdot)+(\cdot,\cdot)_{\mu}$, through $h$-transform. For a certain potential $\mu$, an analytic characterization of these properties is given in terms of the bottom of spectrum.