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Gaussian bounds of heat kernels for Schrödinger operators on Riemannian manifolds
Author(s) -
Takeda Masayoshi
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdl016
Subject(s) - mathematics , heat kernel , riemannian manifold , gaussian , operator (biology) , kernel (algebra) , manifold (fluid mechanics) , schrödinger's cat , pure mathematics , class (philosophy) , gaussian measure , mathematical analysis , quantum mechanics , physics , mechanical engineering , biochemistry , chemistry , repressor , artificial intelligence , computer science , transcription factor , engineering , gene
Suppose that the heat kernel on a complete Riemannian manifold satisfies global Gaussian bounds. We consider a Schrödinger operator for which the potential is a signed measure in a certain Kato class, and we establish a necessary and sufficient condition that the heat kernel of the Schrödinger operator also possesses the global Gaussian bounds.