1998/01/01 by W. G. Cochran, Hui-Hsiung Kuo, Ambar N. Sengupta · 1 citation
Computer Science · #Image and Signal Denoising Methods #Digital Filter Design and Implementation
paper · doi:10.1142/s0219025798000053
openalex publication_date 1998/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 L 2 -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.