Abstract
The quantum white noise (QWN) Gaussian kernel operators (with operators parameters) acting on nuclear algebra of white noise operators is introduced by means of QWN- symbol calculus. The quantum-classical correspondence is studied. An integral representation in terms of the QWN- derivatives and their adjoints is obtained. Under some conditions on the operators parameters, we show that the composition of the QWN-Gaussian kernel operators is a QWN-Gaussian kernel operator with other parameters. Finally, we characterize the QWN-Gaussian kernel operators using important connection with the QWN- derivatives and their adjoints.
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