Generalized Appell Systems
Yuri Kondratiev, Jose Luis Silva, Ludwig Streit
TL;DR
This paper develops a broad framework for infinite-dimensional non-Gaussian analysis by constructing biorthogonal systems and Gel'fand triples for various measures, including Poisson-type measures.
Contribution
It introduces a generalized approach to non-Gaussian analysis in infinite dimensions, extending previous work and providing new tools for measure-based analysis.
Findings
Constructed biorthogonal systems for given measures
Analyzed properties of the generated Gel'fand triples
Applied framework to Poisson-type measures
Abstract
We give a general approach to infinite dimensional non-Gaussian analysis which generalizes the work \cite{KSWY95}. For given measure we construct a family of biorthogonal systems. We study their properties and their Gel'fand triples that they generate. As an example we consider the measures of Poisson type.
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Taxonomy
TopicsStatistical Mechanics and Entropy · Advanced Thermodynamics and Statistical Mechanics · Control Systems and Identification