Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ANALYTIC FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION OF FUNCTIONALS IN A GENERALIZED FRESNEL CLASS

  • Kim, Byoung Soo (School of Liberal Arts Seoul National University of Technology) ;
  • Song, Teuk Seob (Department of Computer Engineering Mokwon University) ;
  • Yoo, Il (Department of Mathematics Yonsei University)
  • Received : 2009.06.02
  • Accepted : 2009.08.14
  • Published : 2009.09.30
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Abstract

Huffman, Park and Skoug introduced various results for the $L_{p}$ analytic Fourier-Feynman transform and the convolution for functionals on classical Wiener space which belong to some Banach algebra $\mathcal{S}$ introduced by Cameron and Storvick. Also Chang, Kim and Yoo extended the above results to an abstract Wiener space for functionals in the Fresnel class $\mathcal{F}(B)$ which corresponds to $\mathcal{S}$. Moreover they introduced the $L_{p}$ analytic Fourier-Feynman transform for functionals on a product abstract Wiener space and then established the above results for functionals in the generalized Fresnel class $\mathcal{F}_{A1,A2}$ containing $\mathcal{F}(B)$. In this paper, we investigate more generalized relationships, between the Fourier-Feynman transform and the convolution product for functionals in $\mathcal{F}_{A1,A2}$, than the above results.

Keywords

References

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