Intrinsic ultracontractivity and small perturbation for one-dimensional generalized diffusion operators |
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Authors: | Matsuyo Tomisaki |
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Institution: | Department of Mathematics, Nara Women's University, Kita-Uoya Nishimachi, Nara 630-8506, Japan |
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Abstract: | We consider a one-dimensional generalized diffusion operator G on an open interval which is not necessarily bounded. We characterize SP] (i.e., 1 is a small perturbation of the operator G) 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). |
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Keywords: | Martin boundary Intrinsic ultracontractivity Semismall perturbation Generalized diffusion operator |
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