Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION PRODUCT OVER WIENER PATHS IN ABSTRACT WIENER SPACE: AN Lp THEORY

  • Published : 2004.03.01
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Abstract

In this paper, using a simple formula, we evaluate the conditional Fourier-Feynman transforms and the conditional convolution products of cylinder type functions, and show that the conditional Fourier-Feynman transform of the conditional convolution product is expressed as a product of the conditional Fourier-Feynman transforms. Also, we evaluate the conditional Fourier-Feynman transforms of the functions of the forms exp {$\int_{O}^{T}$ $\theta$(s,$\chi$(s))ds}, exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))ds}$\Phi$($\chi$(T)), exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))d${\zeta}$(s)}, exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))d${\zeta}$(s)}$\Phi$($\chi$(T)) which are of interest in Feynman integration theories and quantum mechanics.

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  2. CONDITIONAL INTEGRAL TRANSFORMS AND CONVOLUTIONS OF BOUNDED FUNCTIONS ON AN ANALOGUE OF WIENER SPACE vol.26, pp.2, 2013, https://doi.org/10.14403/jcms.2013.26.2.323
  3. Conditional integral transforms and conditional convolution products on a function space vol.23, pp.6, 2012, https://doi.org/10.1080/10652469.2011.596482
  4. Analytic Feynman integrals of transforms of variation of cylinder type functions over Wiener paths in abstract Wiener space vol.3, pp.3, 2005, https://doi.org/10.2478/BF02475918
  5. A TIME-INDEPENDENT CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION PRODUCT ON AN ANALOGUE OF WIENER SPACE vol.35, pp.2, 2013, https://doi.org/10.5831/HMJ.2013.35.2.179
  6. CONDITIONAL FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS OF UNBOUNDED FUNCTIONS ON A GENERALIZED WIENER SPACE vol.50, pp.5, 2013, https://doi.org/10.4134/JKMS.2013.50.5.1105
  7. A TRANSLATION THEOREM FOR THE GENERALIZED FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PROCESS ON FUNCTION SPACE vol.53, pp.5, 2016, https://doi.org/10.4134/JKMS.j150317