## Annals of Functional Analysis

### Applications of an analogue of conditional Wiener integrals

#### Abstract

In this paper, we obtain formulas for the analogue of conditional Wiener integrals for the functional $F$ of the form $$F(x) = \exp\Big\{ \int_{0}^{T} V(x(t)) dt \Big\}, \quad x\in C[0,T]$$ where $V: \Bbb{R} \rightarrow \Bbb{R}$ is a potential function. We then apply this formula to obtain several integration formulas for the functionals involving various potential functions which is used in quantum mechanics and other physical theories.

#### Article information

Source
Ann. Funct. Anal., Volume 6, Number 2 (2015), 116-132.

Dates
First available in Project Euclid: 19 December 2014

https://projecteuclid.org/euclid.afa/1418997771

Digital Object Identifier
doi:10.15352/afa/06-2-11

Mathematical Reviews number (MathSciNet)
MR3292520

Zentralblatt MATH identifier
1347.60098

#### Citation

Lee, Il Yong; Chung, Hyun Soo; Chang, Seung Jun. Applications of an analogue of conditional Wiener integrals. Ann. Funct. Anal. 6 (2015), no. 2, 116--132. doi:10.15352/afa/06-2-11. https://projecteuclid.org/euclid.afa/1418997771

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