Affiliation:
1. Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA
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.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
38 articles.
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