Representation of regularized traces of operators by functional integrals (Q1930822)

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.