Characterization of intrinsic ultracontractivity for one dimensional Schrödinger operators

Abstract

Abstract We consider a Schrodinger operator L = − d 2 / d x 2 + V ( x ) on R , where V is a real-valued measurable function, and give an explicit and simple characterization of intrinsic ultracontractivity (IU) of the Schrodinger semigroup generated by L for a wide class of potentials. By making use of it, we also give new examples of potentials for which the semigroups satisfy (IU) or non-(IU).