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Contents of PMS, Vol. 33, Fasc. 2,
pages 435 - 450
 

CONVOLUTIONS OF GENERALIZED WHITE NOISE FUNCTIONALS

Un Cig Ji
Young Yi Kim
Yoon Jung Park

Abstract: 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.

2000 AMS Mathematics Subject Classification: Primary: 60H40; Secondary: 46F25. Keywords and phrases: White noise theory, convolution, generalized Fourier–Gauss transform, generalized Fourier–Mehler transform.

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