Event
01_1
| 제출번호(No.) | 0068 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Analysis (AN) |
| 영문제목 (Title(Eng.)) |
A Banach algebra over continuous paths with drifts |
| 저자(Author(s)) |
Dong Hyun Cho1 Kyonggi University1 |
| 초록본문(Abstract) | Let $C[0,T]$ denote a generalized analogue of Wiener space, that is, the space of continuous real-valued functions on $[0,T]$, and $C_0[0,T]$ denote the classical Wiener space which is a subspace of $C[0,T]$ satisfying $x(0)=0$ for all $x\in C_0[0,T]$. On this space $C_0[0,T]$, Cameron and Storvick introduced a Banach algebra $\mathcal S$ which is a space of generalized Fourier-Stieltjes transforms of the measures on $L^2[0,T]$. In this talk, we introduce a Banach algebra $S_{\alpha,\beta;\varphi}$ on $C[0,T]$ which is more general than $\mathcal S$, where $\alpha$, $\beta$ and $\varphi$ are the mean function, the variance function and the initial distribution of the paths in $C[0,T]$, respectively. We also investigate its properties, and relationships between it and the Fresnel class which plays a significant role in Feynman integration theories and quantum mechanics. |
| 분류기호 (MSC number(s)) |
28C20 |
| 키워드(Keyword(s)) | Banach algebra, continuous path, drift, Feynman integral |
| 강연 형태 (Language of Session (Talk)) |
Korean |