Integral Representation of Second Quantization and Its Application to White Noise Analysis

✍ Scribed by Y.J. Lee

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 779 KB
• Volume: 133
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1995.1125

✦ Synopsis

It is shown that the second quantization (\Gamma(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 (\mu) 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, (\boldsymbol{h}) and (\mathscr{E}), introduced respectively by Meyer and Yan and by Lee. It is also shown that every member in . (U) has an analytic version in (\mathscr{E}). As a consequence of the equivalence of (\mathscr{H}) and (\mathscr{E}), we show that positive generalized functionals in. (\mathscr{H}^{*}) can be represented by finite measures with exponentially integrable property. 1995 Academic Press. Inc.