The Characterization Of B-valued Generalized Functional By Bargmann-Segal Space

Vector-valued generalized functionals of white noise play an important role in white noise theory. In this paper, we introduce a Banach-valued Bargmann-Segal space E~2(v. X),where v is the complex Gauss measure in generalized functional space E_C~*, X is a complex separable reflexive Banach space. We use the totality of exponential vectors set{?(?);? ? D_p} to discuss the analytic characterization of Banach-valued generalized functional L[G_P,X] via E~2(v, X),where p?R. In addi-tion, we calculus the norm of exponential generalized operators by means of Hilbert operators norm.In addition,we prove that for any X-valued function (?) which satisfies the special condition,there will exist a unique generalized functional accordingly.