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Generalized analytic Fourier-Feynman transforms and convolutions on a Fresnel type class

이일용|장승준
대한수학회 (The Korean Mathematical Society)|2011.03|대한수학회보 (Bulletin of the KMS)|제48권 제2호|pp. 223-245

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convolution productFresnel type classgeneralized Brownian motion processgeneralized analytic Feynman integralgeneralized analytic Fourier-Feynman transform
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초록

In this paper, we define an L_p analytic generalized Fourier-Feynman transform and a convolution product of functionals in a Banach algebra F (C_a,b[0, T]) which is called the Fresnel type class, and in more general class F_A1,_A2} of functionals defined on general function space C_a,b[0, T] rather than on classical Wiener space. Also we obtain some relationships between the L_p analytic generalized Fourier-Feynman transform and convolution product for functionals F (C_a,b[0, T]) and in F_A1,_A2.

Abstract

In this paper, we define an L_p analytic generalized Fourier-Feynman transform and a convolution product of functionals in a Banach algebra F (C_a,b[0, T]) which is called the Fresnel type class, and in more general class F_A1,_A2} of functionals defined on general function space C_a,b[0, T] rather than on classical Wiener space. Also we obtain some relationships between the L_p analytic generalized Fourier-Feynman transform and convolution product for functionals F (C_a,b[0, T]) and in F_A1,_A2.

참고문헌 (22)

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