General characterization theorems and intrinsic topologies in white noise analysis
| dc.creator | Asai, Nobuhiro | |
| dc.creator | Kubo, Izumi | |
| dc.creator | Kuo, Hui-Hsiung | |
| dc.date | 2001-04-12 | |
| dc.date.accessioned | 2026-07-07T04:41:16Z | |
| dc.date.available | 2026-07-07T04:41:16Z | |
| dc.description | Let $u$ be a positive continuous function on $[0, \infty)$ satisfying the conditions: (i) $\lim_{r\to\infty} r^{-1/2}\log u(r)=\infty$, (ii) $\inf_{r\geq 0} u(r)=1$, (iii) $\lim_{r\to \infty}\break r^{-1}\log u(r)<\infty$, (iv) the function $\log u(x^{2}), x\geq 0$, is convex. A Gel'fand triple $[\ce]_{u} \subset (L^{2}) \subset [\ce]_{u}^{*}$ is constructed by making use of the Legendre transform of $u$ discussed in \cite {akk3}. We prove a characterization theorem for generalized functions in $[\ce]_{u}^{*}$ and also for test functions in $[\ce]_{u}$ in terms of their $S$-transforms under the same assumptions on $u$. Moreover, we give an intrinsic topology for the space$[\ce]_{u}$ of test functions and prove a characterization theorem for measures. We briefly mention the relationship between our method and a recent work by Gannoun et al.\cite{ghor}. Finally, conditions for carrying out white noise operator theory and Wick products are given. | |
| dc.description | To appear in Hiroshima Math. J. 31, Louisiana state university preprint (2000) | |
| dc.identifier | https://arxiv.org/abs/math/0104133 | |
| dc.identifier | http://arxiv.org/abs/math/0104133 | |
| dc.identifier | Hiroshima Math. J. 31 (2001) pp299--330 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61291 | |
| dc.subject | Functional Analysis | |
| dc.subject | Probability | |
| dc.subject | 60H40 | |
| dc.title | General characterization theorems and intrinsic topologies in white noise analysis | |
| dc.type | text |