Abstract
In this paper, we introduce a space of theta-admissible distributions denoted by A(theta)* as well as the notion of theta-admissible operators. We study the regularity properties of the classical conditional expectation acting on A(theta)* and acting on L(A(theta), A(theta)*) which is the space of linear continuous operators from A(theta) into A(theta)*. An integral representation with respect to the coordinate system of the quantum white noise (QWN) derivatives and their adjoints {D-t(+/-), D-t(+/-)*, t is an element of R} of such conditional expectation is given. Then, we give a quantum white noise counterpart of the Clark formula. Finally, we introduce the QWN Hitsuda-Skorokhod integrals. Such integrals are shown to be QWN martingales using a new notion of QWN conditional expectation.