Abstract
we develop an operator theory on a nuclear algebra of white noise operators in terms of the quantum white noise (QWN) derivatives and their dual adjoints. Using an adequate definition of a QWN-symbol transformation, we discuss QWN-integral-sum kernel operators which give the Fock expansion of the QWN-operators (i.e. the linear operators acting on nuclear algebra of white noise operators). As application, we characterize all rotation invariant QWN-operators by means of the QWN-conservation operator, the QWN-Gross Laplacians. These topics are expected to open a new area in QWN infinite-dimensional analysis.
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