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Using a simple formula for conditional expectations over an analogue of Wiener space, we calculate a generalized analytic conditional Fourier-Feynman transform and convolution product of generalized cylinder functions which play important roles in Feynman integration theories and quantum mechanics. We then investigate their relationships, that is, the conditional Fourier-Feynman transform of the convolution product can be expressed in terms of the product of the conditional Fourier-Feynman transforms of each function. Finally we establish change of scale formulas for the generalized analytic conditional Fourier-Feynman transform and the conditional convolution product. In this evaluation formulas and change of scale formulas we use multivariate normal distributions so that the orthonormalization process of projection vectors which are essential to establish the conditional expectations, can be removed in the existing conditional Fourier-Feynman transforms, conditional convolution products and change of scale formulas.
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참고문헌 (12)
참고문헌 신청
B. S. Kim / 2015 / Relationships between generalized Wiener integrals and condi-tional analytic Feynman integrals over continuous paths / Czechoslovak Math. J
D. H. Cho / 2014 / Analogues of conditional Wiener integrals with drift and initial distribution on a function space / Abstr. Appl. Anal 2014 : 12 ~
D. H. Cho / 2015 / A present position-dependent conditional Fourier-Feynman transform and convolution product over continuous paths / Int. J. Math. Anal. (Ruse) 9 (48) : 2387
D. H. Cho / 2016 / Integral transforms on a function space with change of scales using multivariate normal distributions / J. Funct. Spaces 2016 : 9 ~
Dong Hyun Cho / 2016 / Change of scale formulas for a generalized conditional Wiener integral / 대한수학회보 53 (5) : 1531 ~ 1548
D. H. Cho / 2014 / Analogues of conditional Wiener integrals with drift and initial distribution on a function space / Abstr. Appl. Anal 2014 : 12 ~
D. H. Cho / 2015 / A present position-dependent conditional Fourier-Feynman transform and convolution product over continuous paths / Int. J. Math. Anal. (Ruse) 9 (48) : 2387
D. H. Cho / 2016 / Integral transforms on a function space with change of scales using multivariate normal distributions / J. Funct. Spaces 2016 : 9 ~
Dong Hyun Cho / 2016 / Change of scale formulas for a generalized conditional Wiener integral / 대한수학회보 53 (5) : 1531 ~ 1548
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