Mathematica Eterna
Open Access

Abstract

A Survey of an Analog of Analytic Feynman Integrals on a Function Space

Myung Jae Kim

Let C r [0, t] denote an analogue of the r-dimensional Wiener space. In the present paper, we introduce analogues of the analytic Wiener and Feynman integrals for several types of functions, in particular, the functionals of the forms expZ t 0 θ(s, x(s))dη(s)  ψ(x(t)) and Xr j=1 Z t 0 (xj (s))mjds for x = (x1, · · · , xr) ∈ C r [0, t], where η is a complex Borel measure on [0, t], and θ(s, ·) and ψ are the Fourier-Stieltjes transforms of the complex Borel measures on the r-dimensional Euclidean space R r .

Published Date: 2018-09-05;