Learn the basics of white noise theory with White Noise Distribution Theory. This book
covers the mathematical foundation and key applications of white noise theory without …

In the recent years Hida's white noise calculus [8] has been established as a Schwartz type
distribution theory on Gaussian space by many authors, for instance, Kubo and Takenaka …

A recurrent theme in functional analysis is the interplay between the theory of positive
definite functions and their reproducing kernels on the one hand, and Gaussian stochastic …

A generalized Laplacian ΔG (K) is defined as a continuous linear operator acting on the
space of test white noise functionals. Operator-parameter-and-transforms on white noise …

In this paper we first construct a two-parameter transformation group G on the space of test
white noise functionals in which the adjoints of Kuo's Fourier and Kuo's Fourier—Mehler …

February 9, 1999 15:20 WSPC/102-IDAQPRT 0019 CAUCHY PROBLEMS ASSOCIATED WITH
THE LÉVY LAPLACIAN IN WHITE NOISE ANALYSIS 1. Intr Page 1 February 9, 1999 15:20 …

Eigenfunctions of the Lévy Laplacian with an arbitrary real number as an eigenvalue are
constructed by means of a coordinate change of white noise distributions. The Lévy …

We first study the generalized Fourier-Gauss transforms of functionals defined on the
complexification BC of an abstract Wiener space (H, B, ν). Secondly, we introduce a new …

We study shifted generalized Mehler semigroups on white noise functionals. We prove
characterizations of invariant (white noise) distribution and the covariance property for …

Recent developments in quantum white noise calculus are outlined on the basis of various
characterization theorems for operator symbols. A quantum stochastic integral and a …