Year: 2004
Type: preprint
Abstract: It is known that many constructions arising in the classical Gaussian infinite dimensional analysis can be extended to the case of more general measures. One such extension can be obtained through biorthogonal systems of Appell polynomials and generalized functions. In this paper, we consider linear continuous operators from a nuclear Frechet space of test functions to itself in this more general setting. We construct an isometric integral transform (biorthogonal CS-transform) of those operators into the space of germs of holomorphic functions on a locally convex infinite dimensional nuclear space. Using such transform, we provide characterization theorems and give biorthogonal chaos expansion for operators.
Source: arXiv (Cornell University)
Author: Yablonsky, Eugene
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1558062946