广义维纳泛函,白噪声分布及实Schwartz广义函数空间上的分布

摘要

在实Schwartz广义函数空间上,证明了复值广义维纳泛函, 由Kondratev-Streit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 Schwartz space ofgeneralized functions, we will prove that complex generalized Wienerfunctionals and complex white noise distributions constructed byKondratev-Streit and Hida are all distributions constructed byKhrennikov. Using the above result we also prove that a class ofinfinite dimensional pseudodifferential operators (i.e.Ψ DO'S) consists of extensions of continuous linear operators on thespace of complex generalized Wiener functionals. Moreover, we prove thatthe space of test functions for distributions constructed by Khrennikovis a subspace of Meyer--Yan space of white noise test functionals.