A TIME-INDEPENDENT CONDITIONAL FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION PRODUCT ON AN ANALOGUE OF WIENER SPACE

Cho, Dong Hyun

• 투고 : 2013.03.18
• 심사 : 2013.04.29
• 발행 : 2013.06.25
• 28 3

초록

Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $X_n:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ by $Xn(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t$ is a partition of $[0,t]$. In the present paper, using a simple formula for the conditional expectation given the conditioning function $X_n$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transform and the conditional convolution product of the cylinder functions which have the form $$f((v_1,x),{\cdots},(v_r,x))\;for\;x{\in}C[0,t]$$, where {$v_1,{\cdots},v_r$} is an orthonormal subset of $L_2[0,t]$ and $f{\in}L_p(\mathbb{R}^r)$. We then investigate several relationships between the conditional Fourier-Feynman transform and the conditional convolution product of the cylinder functions.

키워드

analogue of Wiener measure;analytic conditional Feynman integral;analytic conditional Fourier-Feynman transform;analytic conditional Wiener integral;conditional convolution product

참고문헌

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피인용 문헌

1. CONDITIONAL FOURIER-FEYNMAN TRANSFORMS AND CONVOLUTIONS OF UNBOUNDED FUNCTIONS ON A GENERALIZED WIENER SPACE vol.50, pp.5, 2013, https://doi.org/10.5831/HMJ.2013.35.2.179

과제정보

연구 과제 주관 기관 : Kyonggi University