대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제26권2호
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  • Pages.273-289
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  • 2011
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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CONDITIONAL GENERALIZED FOURIER-FEYNMAN TRANSFORM OF FUNCTIONALS IN A FRESNEL TYPE CLASS

  • 투고 : 2010.04.03
  • 발행 : 2011.04.30
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초록

In this paper we dene the concept of a conditional generalized Fourier-Feynman transform on very general function space $C_{a,b}$[0, T]. We then establish the existence of the conditional generalized Fourier-Feynman transform for functionals in a Fresnel type class. We also obtain several results involving the conditional transform. Finally we present functionals to apply our results. The functionals arise naturally in Feynman integration theories and quantum mechanics.

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참고문헌

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피인용 문헌

  1. GENERALIZED FOURIER-FEYNMAN TRANSFORM AND SEQUENTIAL TRANSFORMS ON FUNCTION SPACE vol.49, pp.5, 2012, https://doi.org/10.4134/JKMS.2012.49.5.1065
  2. Effect of drift of the generalized Brownian motion process: an example for the analytic Feynman integral vol.106, pp.6, 2016, https://doi.org/10.1007/s00013-016-0899-x