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

2011/05/04 by Batu Güneysu, Güneysu, Batu
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Random Matrices and Applications #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1105.0748

openalex publication_date 2011/05/04 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We define and examine certain matrix-valued multiplicative functionals with\nlocal Kato potential terms and use probabilistic techniques to prove that the\nsemigroups of the corresponding partial differential operators with\nmatrix-valued coefficients are spatially continuous and have a jointly\ncontinuous integral kernel. These partial differential operators include\nYang-Mills type Hamiltonians and Pauli type Hamiltonians, with "electrical"\npotentials that are elements of the matrix-valued local Kato class.\n

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