Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2009; 24(3): 397-413

Printed September 1, 2009

https://doi.org/10.4134/CKMS.2009.24.3.397

Copyright © The Korean Mathematical Society.

Transforms and convolutions on function space

Seung Jun Chang and Jae Gil Choi

Dankook University

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In this paper, for functionals of a generalized Brownian motion process, we show that the generalized Fourier-Feynman transform of the convolution product is a product of multiple transforms and that the conditional generalized Fourier-Feynman transform of the conditional convolution product is a product of multiple conditional transforms. This allows us to compute the (conditional) transform of the (conditional) convolution product without computing the (conditional) convolution product.

Keywords: generalized Brownian motion process, generalized Fourier-Feynman transform, convolution product, conditional generalized Fourier-Feynman transform, conditional convolution product

MSC numbers: Primary 60J65, 28C20

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