Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2013; 50(5): 1105-1127

Printed September 1, 2013

https://doi.org/10.4134/JKMS.2013.50.5.1105

Copyright © The Korean Mathematical Society.

Conditional Fourier-Feynman transforms and convolutions of unbounded functions on a generalized Wiener space

Dong Hyun Cho

Kyonggi University

Abstract

Let $C[0, t]$ denote the function space of real-valued continuous paths on $[0, t]$. Define $X_{n}: C[0, t]\to \mathbb R^{n+1}$ and $X_{n+1}: C[0, t]\to \mathbb R^{n+2}$ by $X_n(x) = (x(t_0), x(t_1), $ $\ldots, x(t_n)) $ and $ X_{n+1}(x) = (x(t_0), x(t_1), $ $ \ldots,x (t_n), $ $x(t_{n+1}))$, respectively, where $0=t_0 < t_1 < \cdots < t_n

Keywords: analogue of Wiener space, analytic conditional Feynman integral, analytic conditional Fourier-Feynman transform, analytic conditional Wiener integral, conditional convolution product, Wiener space

MSC numbers: Primary 28C20