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In this paper we define a generalized analytic Fourier--Feyn\-man transform associated with Gaussian process on the function space $C_{a,b}[0,T]$. We establish the existence of the generalized analytic Fourier--Feynman transform for certain bounded functionals on $C_{a,b}[0,T]$. We then proceed to establish a translation theorem for the generalized transform associated with Gaussian process.
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참고문헌 (32)
참고문헌 신청
J. M. Ahn / 2003 / Fourier–Feynman transform, convolution and first variation / Acta Math. Hungar 100(3):215~235
J. M. Ahn / 2006 / Multiple Lp Fourier–Feynman transforms on abstract Wiener space / Integral Transforms Spec. Funct 17(1):1~26
M. D. Brue / 1972 / A functional transform for Feynman integrals similar to the Fourier transform
R. H. Cameron / 1951 / Additional functionals on a space of continuous functions. I / Trans. Amer. Math. Soc 70(1):160~176
R. H. Cameron / 1944 / Transformations of Wiener integrals under translations / Ann. of Math 45(2):386~396
J. M. Ahn / 2006 / Multiple Lp Fourier–Feynman transforms on abstract Wiener space / Integral Transforms Spec. Funct 17(1):1~26
M. D. Brue / 1972 / A functional transform for Feynman integrals similar to the Fourier transform
R. H. Cameron / 1951 / Additional functionals on a space of continuous functions. I / Trans. Amer. Math. Soc 70(1):160~176
R. H. Cameron / 1944 / Transformations of Wiener integrals under translations / Ann. of Math 45(2):386~396
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