2004/03/01 by Eugene Yablonsky, Yablonsky, Eugene
Mathematics · Physics and Astronomy · #46F25 #60H40 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis #Statistical Mechanics and Entropy #math.FA #msc:46F25 #msc:60H40
paper · pdf · doi:10.48550/arxiv.math/0403025
13 pages
arxiv created 2004/03/01 · openalex publication_date 2004/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.