广义维纳泛函,白噪声分布及实Schwartz广义函数空间上的分布(英文)

Generalized Wiener Functionals, White Noise Distributions, and Distributions on the Real Schwartz Spaces of Generalized Functions

在实Ｓｃｈｗａｔｚ广义函数空间上，证明了复值广义维纳泛函，由Ｋｏｎｄｒａｔｅｖ－ｓｔｒｅｉｄ及Ｈｉｄａ构造的复值白噪声分布都是由Ｋｈｒｅｎｎｉｋｏｖ构造的分布．利用上述结果进而证明了，一类无穷维伪微分算子是由复值广义维纳泛函空间上的连续线性算子族扩张而成．更进一步，还证明了由Ｋｈｒｅｎｎｉｋｏｖ构造的关于分布的试验函数空间是关于白噪声泛函的Ｍｅｙｅｒ－Ｙａｎ试验函数空间的子空间．

On the real Schwsrtz space of generalized functions, we will prove that complex generalized Wiener functioals and complex white noise distributions constructed by Kondratev-Streit and Hida are all distributions constructed by Khrennikov. Using the above result we also prove that a class of infinite dimensional pseudodifferen- tial operators (i.e. DO'S) consists of extensions of continuous linear operators on the space of complex generalized Wiener functionals. Moreover, we prove that the space of test functions for distributions contracted by Khrennikov is a subspace of Meyer-Yan space of white noise test functionals.