Multiplicative matrix-valued functionals and the continuity properties of semigroups corresponding to partial differential operators with matrix-valued coefficients

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:380

Article

Gueneysu, Batu

关键词: Feynman-Kac formula;    Schrodinger operators;    Stochastic differential equations;    Partial differential equations;   

DOI  :  10.1016/j.jmaa.2011.02.038

来源: Elsevier

【 摘 要 】

We define and examine certain matrix-valued multiplicative functionals with local Kato potential terms and use probabilistic techniques to prove that the semigroups of the corresponding self-adjoint partial differential operators with matrix-valued coefficients map from L-2(R-n, C-d) to the space of continuous bounded functions, and that these semigroups have a jointly continuous and spatially bounded integral kernel. These partial differential operators include Yang-Mills type Hamiltonians with electrical potentials that are elements of the matrix-valued local Kato class. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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