Abstract
In this paper we dene the concept of a conditional generalized Fourier-Feynman transform on very general function space <TEX>$C_{a,b}$</TEX>[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.
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