Transforms and convolutions on function space
Commun. Korean Math. Soc. 2009 Vol. 24, No. 3, 397-413
https://doi.org/10.4134/CKMS.2009.24.3.397
Printed September 1, 2009
Seung Jun Chang and Jae Gil Choi
Dankook University
Abstract : 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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