Behaviour of the first variation under a Fourier-Feynman transform for cylinder functions on Wiener spaces II

作者：Kim Young Sik^*

来源：Integral Transforms and Special Functions, 2010, 21(1): 13-23.

DOI：10.1080/10652460902945100

• Wiener space
• Wiener integral
• first variation
• Fourier-Feynman transforms

We investigate the behaviour of the first variation of certain cylinder-type functions: [image omitted] under the Fourier-Feynman transform, where [image omitted] is a Fourier transform of the measure on Rn of the form [image omitted] and {1, 2, ..., n} is an orthonormal class of L2[0, T] and [image omitted] and [image omitted] are in Rn. And we show that the first variation of [image omitted] behave nicely under Fourier-Feynman transforms. And we show that the Fourier-Feynman transform of the first variation of [image omitted] can be perfectly expressed as the limit of a sequence of Wiener integrals of the first variation on the Wiener space.

• 出版日期2010