Representation of regularized traces of operators by functional integrals
type: Item
instance of: scholarly article
title: Representation of regularized traces of operators by functional integrals
zbMATH Open document ID: 1263.47058
DOI: 10.1134/S1064562412050316
author: O. G. Smolyanov
author: V. A. Sadovnichy
author: Eugene T. Shavgulidze
published in: Doklady Mathematics
publication date: 2013-01-14T00:00:00Z
review text: From the introduction: In this paper, we obtain representations for the regularized traces [\textit{V. A. Sadovnichii}, Operator theory (Теория операторов. Учебное пособие). Moskva: Izdatel'stvo Moskovskogo Universiteta (1979; Zbl 0517.47001)] of simplest second order differential operators by using functional integrals and give examples of applications of these representations to obtain formulas not containing functional integrals. Possible approximations of these infinite-dimensional integrals by finite dimensional ones, i.e., analogues of Feynman formulas, are also discussed. The exposition is of formal character at some places, and some analytical assumptions are omitted.
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 6124969
zbMATH Keywords: functional integrals
zbMATH Keywords: representation of regularized traces
zbMATH Keywords: Chernoff's formula
reviewed by: Rodica Luca
MaRDI profile type: Publication
cites work: One-Parameter Semigroups for Linear Evolution Equations
cites work: Hamiltonian Feynman path integrals via the Chernoff formula
cites work: Feynman formulas generated by self-adjoint extensions of the Laplacian
cites work: Chernoff's theorem and discrete time approximations of Brownian motion on manifolds
cites work: Q3872705
full work available at URL: s1064562412050316
OpenAlex ID: W2117933088
description: scientific article; zbMATH DE number 6124969