Academician V. A. Sadovnichii, O. G. Smolyanov, and E. T. Shavgulidze
Received August 28, 2015
Abstract—Representations of regularized determinants of elements of one-parameter operator semigroups
whose generators are second-order elliptic differential operators by Lagrangian functional integrals are
obtained. Such semigroups describe solutions of inverse Kolmogorov equations for diffusion processes. For
self-adjoint elliptic operators, these semigroups are often called Schrödinger semigroups, because they are
obtained by means of analytic continuation from Schrödinger groups. It is also shown that the regularized deter-
minant of the exponential of the generator (this exponential is an element of a one-parameter semigroup) coin-
cides with the exponential of the regularized trace of the generator.
DOI: 10.1134/S1064562416010166
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