Quantum white noise Gaussian kernel operators

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.