A new class of white noise generalized functions
The S-transform is studied as a mapping from a space of tensors to a space of functions over a complex space. The range of this transform is characterized in terms of analyticity and growth. These results are applied to a broad class of generalized functions in white noise analysis. These correspond to completions of the Gaussian L2-space which preserve orthogonality of Hermite polynomials. The S-transform is defined for the new generalized functions, and the range of this S-transform is identified in terms of analyticity and growth. Examples of the new spaces of generalized functions are given; these include distributions considered by Kondratiev and Streit, as well as new classes of distributions whose S-transforms have growth bounded by iterated exponentials.
Publication Source (Journal or Book title)
Infinite Dimensional Analysis, Quantum Probability and Related Topics
Cochran, W., Kuo, H., & Sengupta, A. (1998). A new class of white noise generalized functions. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 1 (1), 43-67. https://doi.org/10.1142/S0219025798000053