A TRANSLATION THEOREM FOR THE GENERALIZED FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PROCESS ON FUNCTION SPACE

作者：Chang Seung Jun^*; Choi Jae Gil; Ko Ae Young

来源：Journal of the Korean Mathematical Society, 2016, 53(5): 991-1017.

DOI：10.4134/JKMS.j150317

• generalized Brownian motion process
• Gaussian process
• generalized analytic Feynman integral
• generalized analytic Fourier-Feynman transform
• translation theorem.

In this paper we define a generalized analytic Fourier-Feynman transform associated with Gaussian process on the function space C-a,C- b [0,T]. We establish the existence of the generalized analytic Fourier Feynman transform for certain bounded functionals on C-a,C- b [0, T]. We then proceed to establish a translation theorem for the generalized transform associated with Gaussian process.

• 出版日期2016-9