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MULTIPLE Lp ANALYTIC GENERALIZED FOURIER-FEYNMAN TRANSFORM ON THE BANACH ALGEBRA

  • Published : 2004.01.01

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 Lp analytic generalized Fourier-Feynman transform and the generalized convolution product of functional on function space $C_{a,\;b}[0,\;T]$. We then verify the existence of the multiple $L_{p}$ analytic generalized Fourier-Feynman transform for functional on function space that belong to a Banach algebra $S({L_{a,\;b}}^{2}[0, T])$. Finally we establish some relationships between the multiple $L_{p}$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $S({L_{a,\;b}}^{2}[0, T])$.ヨ⨀

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

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  1. CONDITIONAL GENERALIZED FOURIER-FEYNMAN TRANSFORM OF FUNCTIONALS IN A FRESNEL TYPE CLASS vol.26, pp.2, 2011, https://doi.org/10.4134/CKMS.2011.26.2.273
  2. GENERALIZED ANALYTIC FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS ON A FRESNEL TYPE CLASS vol.48, pp.2, 2011, https://doi.org/10.4134/BKMS.2011.48.2.223
  3. CHANGE OF SCALE FORMULAS FOR FUNCTION SPACE INTEGRALS RELATED WITH FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION ON Ca,b[0, T] vol.23, pp.1, 2015, https://doi.org/10.11568/kjm.2015.23.1.47