Intrinsic ultracontractivity and small perturbation for one-dimensional generalized diffusion operators

摘要

We consider a one-dimensional generalized diffusion operator g on an open interval which is not necessarily bounded. We characterize [SP] (i.e., I is a small perturbation of the operator 9) in terms of the classification of the boundary points from the view point of diffusion processes and give a sufficient condition for [IU] (i.e., the associated heat kernel is intrinsically ultracontractive). (c) 2007 Elsevier Inc. All rights reserved.