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.