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J. Korean Math. Soc. 2004; 41(2): 319-344

Printed March 1, 2004

Copyright © The Korean Mathematical Society.

Conditional integrals on abstract wiener and Hilbert spaces with application to Feynman integrals

Dong Myung Chung, Soon Ja Kang, and Kyung Pil Lim

Sogang University, Chonnam National University, Sogang University

Abstract

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In this paper, we define conditional integrals on abstract Wiener and Hilbert spaces and then obtain a formula for evaluating the integrals. We use this formula to establish the existence of conditional Feynman integrals for the classes $\Lambda^q(B)$ and $\Lambda^q(H)$ of functions on abstract Wiener and Hilbert spaces and then specialize this result to provide the fundamental solution to the Schr\"{o}dinger equation with the forced harmonic oscillator.

Keywords: Feynman integrals, conditional analytic Feynman integral, abstract Wiener space, lifting, fundamental solution

MSC numbers: 28C20

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