55 research outputs found
Multiplicative matrix-valued functionals and the continuity properties of semigroups correspondings to partial differential operators with matrix-valued coefficients
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 partial differential operators with
matrix-valued coefficients are spatially continuous and have a jointly
continuous integral kernel. These partial differential operators include
Yang-Mills type Hamiltonians and Pauli type Hamiltonians, with "electrical"
potentials that are elements of the matrix-valued local Kato class.Comment: 26 pages; will appear in a slightly different form in the Journal of
Mathematical Analysis and Application
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