Bulletin of the
Korean Mathematical Society BKMS

In [10], Chang and Skoug used a generalized Brownian motion process to define a generalized analytic Feynman integral and a generalized analytic Fourier-Feynman transform. In this paper we define the conditional generalized Fourier-Feynman transform and conditional generalized convolution product on function space. We then establish some relationships between the conditional generalized Fourier-Feynman transform and conditional generalized convolution product for functionals on function space that belonging to a Banach algebra.

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

MSC numbers: 60J65,28C20