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GENERALIZED ANALYTIC FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS ON A FRESNEL TYPE CLASS

  • Received : 2007.03.17
  • Published : 2011.03.31

Abstract

In this paper, we de ne an $L_p$ analytic generalized Fourier Feynman transform and a convolution product of functionals in a Ba-nach algebra $\cal{F}$($C_{a,b}$[0, T]) which is called the Fresnel type class, and in more general class $\cal{F}_{A_1;A_2}$ of functionals de ned on general functio space $C_{a,b}$[0, T] rather than on classical Wiener space. Also we obtain some relationships between the $L_p$ analytic generalized Fourier-Feynman transform and convolution product for functionals in $\cal{F}$($C_{a,b}$[0, T]) and in $\cal{F}_{A_1,A_2}$.

Keywords

generalized Brownian motion process;generalized analytic Feynman integral;generalized analytic Fourier-Feynman transform;convolution product;Fresnel type class

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