Integral Representation of Second Quantization and Its Application to White Noise Analysis
Integral Representation of Second Quantization and Its Application to White Noise Analysis
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第二量化的积分表示及其在白噪声分析中的应用
DOI：
10.1006/jfan.1995.1125
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发表时间：
1995
影响因子：
1.7
通讯作者：
Yuh
中科院分区：
文献类型：
--
作者：
Yuh
摘要 证明了连续线性算子K在某个核空间E上的第二量子化Г(K)在对偶空间E*上相对于E*上的正则高斯测度μ具有积分表示。采用这种表示，可以获得更清晰的增长估计和白噪声泛函的局部性。我们还在测试白噪声泛函 M 和 E 的两个新空间之间建立了拓扑等价，这两个空间分别由 Meyer 和 Yan 以及 Lee 提出。还表明 M 中的每个成员在 E 中都有一个解析版本。由于 M 和 E 等价，我们证明 M 中的正广义泛函可以用具有指数可积性质的有限测度来表示。
Abstract It is shown that the second quantization Γ( K ) for a continuous linear operator K on a certain nuclear space E enjoys an integral representation on the dual space E * with respect to the canonical Gaussian measure μ on E *. Employing such a representation, sharper growth estimates and locality for white noise functionals are obtained. We also establish a topological equivalence between two new spaces of test white noise functionals M and E , introduced respectively by Meyer and Yan and by Lee. It is also shown that every member in M has an analytic version in E . As a consequence of the equivalence of M and E , we show that positive generalized functionals in M can be represented by finite measures with exponentially integrable property.