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Convolutions of generalized white noise functionals

Ji U. C., Kim Y. Y., Park Y. J.

Probability and Mathematical Statistics

2013

Vol. 33, Fasc. 2

435--450

We study a general definition of convolution products of test white noise functionals, of which the consistency property is examined. As an application of the consistency property of the convolution product we study an extension of the convolution to generalized white noise functionals. We also study relations between the convolution and generalized Fourier-Gauss and generalized Fourier-Mehler transforms.