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dc.contributor.authorLiu, Jingbo
dc.date.accessioned2019-10-15T15:30:25Z
dc.date.available2019-10-15T15:30:25Z
dc.date.issued2019-05-30
dc.identifier.otherLiu_cornellgrad_0058F_11364
dc.identifier.otherhttp://dissertations.umi.com/cornellgrad:11364
dc.identifier.otherbibid: 11050344
dc.identifier.urihttps://hdl.handle.net/1813/67362
dc.description.abstractIn this thesis we study the properties of the Schrodinger operator L=−∆+q on a Harnack-type Dirichlet space for q belonging to Kato class K or Kato-infinity class K∞. To be specific, it consists of three parts as follows: The first part is a generalization of [27]. For any Harnack-type Dirichlet space we give conditions under which there exists a positive Dirichlet solution (the profile) in an unbounded uniform domain for the operator L. In this setting, we further give the two-sided heat kernel estimate using the famous h-transform technique. The idea of second part comes from [64]. In the exterior of a compact set in a non- parabolic Harnack-type space, we can prove some equivalent statements connect- ing subcrilicality, positiveness of the Green function, gaugeability and the bound- edness of the Dirichlet-type solution provided the potential q ∈ K∞. Particularly, we can apply the boundedness result of the profile to the first part and conclude a more precise heat kernel estimate. In the third part we provide some typical examples and explore some properties when the potential decays faster than the quadratic one. Some other examples are given in the domain outside an unbounded domain and we propose some hypothesis as an supplement to the second part.
dc.language.isoen_US
dc.subjectMathematics
dc.subjectDirichlet
dc.subjectHeat Kernel Estimate
dc.subjectUniform Domain
dc.titleHEAT KERNEL ESTIMATE OF THE SCHRODINGER OPERATOR IN UNIFORM DOMAINS
dc.typedissertation or thesis
thesis.degree.disciplineMathematics
thesis.degree.grantorCornell University
thesis.degree.levelDoctor of Philosophy
thesis.degree.namePh.D., Mathematics
dc.contributor.chairSaloff-Coste, Laurent Pascal
dc.contributor.committeeMemberHealey, Timothy James
dc.contributor.committeeMemberCao, Xiaodong
dcterms.licensehttps://hdl.handle.net/1813/59810
dc.identifier.doihttps://doi.org/10.7298/rjgx-5842


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