CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION PRODUCT OVER WIENER PATHS IN ABSTRACT WIENER SPACE

Abstract:

In this paper, we define the conditional Fourier-Feynman transform and the conditional convolution product over Wiener paths in abstract Wiener space. Using a simple formula, we obtain conditional Feynman integrals of Fourier-Feynman transform and convolution product of cylinder type functions. For these functions, we evaluate the conditional Fourier-Feynman transforms and the conditional convolution products, and show that the conditional Fourier-Feynman transform of the conditional convolution product is a product of the conditional Fourier-Feynman transforms.

Keywords: Conditional analytic Feynman integral; Conditional convolution product; Conditional Fourier– Feynman transform; Conditional Wiener integral; Cylinder type function; Simple formula for conditional Wiener integral

Document Type: Research article

DOI: 10.1080/1065246031000081652

Affiliations: 1: Department of Mathematics, Yonsei University, Seoul 120-749, Korea