一族Hida广义泛函的构造及其性质

Structure and Properties of a Family of Hida Generalized Functional

本文证明了当一族可微单参数子群 {gθ}θ∈R+ GL(E) ,其生成元T被看成是H稠定算子时是自其轭时 ,有一族可微单参数子群 {Lθ}θ∈R GL( (E) ) L( (E ,(E) )与此相对应 .由此我们可得到一族正广义泛函Φθx,其相应的测度是一簇转移概率 ,特别地 ,当T=-I时 ,它们是一簇Ornstein Unlenbeck转移概率 .

In this paper,we study a family Hida generalized functional and its properties.Let {g θ} θ∈R +GL(E) be a differentiable one-parameter subgroup with infinitesimal generator T,if T is a selfadjoint operator on H,then there exists a differentiable one-parameter subgroup {L θ} θ∈R +GL((E))L((E),(E)) with respect to it.Furthermore,we can get a family positive generalized functional Φθ x,θ∈R +,and a family P t(x,dy) of probability transition kernels,in particular,if T=-I,then P t(x,dy) is a family Ornstein-Uhlenbeck probability transition kernels