Multiple $L_p$ analytic generalized Fourier-Feynman transform on the Banach algebra
Commun. Korean Math. Soc. 2004 Vol. 19, No. 1, 93-111
Printed March 1, 2004
Seung Jun Chang, Jae Gil Choi
Dankook University, Dankook University
Abstract : In this paper, we use a generalized Brownian motion process to define a generalized Feynman integral and a generalized Fourier-Feynman transform. We also define the concepts of the multiple $L_p$ analytic generalized Fourier-Feynman transform and the generalized convolution product of functionals on function space $\cab$. We then verify the existence of the multiple $L_p$ analytic generalized Fourier-Feynman transform for functionals on function space that belong to a Banach algebra $\sab$. Finally we establish some relationships between the multiple $L_p$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $\sab$.
Keywords : generalized Brownian motion process, generalized analytic Feynman integral, generalized analytic Fourier-Feynman transform, generalized convolution product, multiple $L_p$ analytic generalized Fourier-Feynman transform
MSC numbers : 60J65,28C20
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