A new class of white noise generalized functions
Document Type
Article
Publication Date
1-1-1998
Abstract
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
First Page
43
Last Page
67
Recommended Citation
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