Conditional generalized Fourier-Feynman transform of functionals in a Fresnel type class
Commun. Korean Math. Soc. 2011 Vol. 26, No. 2, 273-289
https://doi.org/10.4134/CKMS.2011.26.2.273
Printed June 1, 2011
Seung Jun Chang
Dankook University
Abstract : In this paper we define the concept of a conditional generalized Fourier-Feynman transform on very general function space $C_{a,b}[0,T]$. We then establish the existence of the conditional generalized Fourier-Feynman transform for functionals in a Fresnel type class. We also obtain several results involving the conditional transform. Finally we present functionals to apply our results. The functionals arise naturally in Feynman integration theories and quantum mechanics.
Keywords : generalized Brownian motion, Fresnel type class, generalized Fourier-Feynman transform, conditional generalized Feynman integral, conditional generalized Fourier-Feynman transform
MSC numbers : Primary 60J65, 28C20
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