The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ASSOCIATED WITH VECTOR-VALUED CONDITIONING FUNCTION

  • Ae Young Ko (Basic Science and Mathematics Center, Dankook University) ;
  • Jae Gil Choi (School of General Education, Dankook University)
  • Received : 2023.01.01
  • Accepted : 2023.02.23
  • Published : 2023.05.31
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Abstract

In this paper, we use a vector-valued 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 functionals which form a Banach algebra. We then provide fundamental relationships between the CFFTs and the CCPs.

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Acknowledgement

The authors would like to express their gratitude to the editor and the referees for their valuable comments and suggestions which have improved the original paper.

References

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