Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ASSOCIATED WITH INFINITE DIMENSIONAL CONDITIONING FUNCTION

  • Jae Gil Choi (School of General Education Dankook University) ;
  • Sang Kil Shim (Department of Mathematics Dankook University)
  • Received : 2022.09.01
  • Accepted : 2022.12.30
  • Published : 2023.09.30
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Abstract

In this paper, we use an infinite dimensional conditioning function to define a conditional Fourier-Feynman transform (CFFT) and a conditional convolution product (CCP) on the Wiener space. We establish the existences of the CFFT and the CCP for bounded functions which form a Banach algebra. We then provide fundamental relationships between the CFFTs and the CCPs.

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References

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