Bargmann-Segal空间刻画Banach空间值广义泛函

The characterization of Banach-valued generalized functional by Banach-valued Bargmann-Segal space

引入Banach空间值Bargmann-Segal空间E2(v,X),其中v是广义函数空间E*C上的复Gauss测度,X是一个可分自反Banach空间.借助于指数向{ε(ξ):ξ∈Dp}的完全性,通过广义算子象征方法,应用E2(v,X)讨论了Banach空间值广义泛函L[Gp,X]的解析刻画,其中p∈R.同时,应用广义泛函在E2(v,X)中的Hilbert范数计算了向量值广义算子T∈L[Gp,X]的算子范数.

The Banach-valued Bargmann-Segal space E2（v,X）is introduced,where vis complex Gauss measure in generalized functional space L[Gp,X],Xis a complex separable reflexive Banach space.The totality of exponential vectors set{ε（ξ）：ξ∈Dp}is used to discuss the analytic characterization of Banachvalued generalized functional via L[Gp,X],where p∈R.Meanwhile,the generalized operator norm is given by means of Hilbert operator norm of generalized functional in E2（v,X）.