Generalized Wright Analysis in Infinite Dimensions

2024/05/02 by Beghin, Luisa, Cristofaro, Lorenzo, da Silva, José L. · 2 citations
#FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2405.01665

Abstract

This paper investigates a broad class of non-Gaussian measures, μ_Ψ, associated with a family of generalized Wright functions, _mΨ_q. First, we study these measures in Euclidean spaces ℝ^d, then define them in an abstract nuclear triple N\subsetH\subsetN'. We study analyticity, invariance properties, and ergodicity under a particular group of automorphisms. Then we show the existence of an Appell system which allows the extension of the non-Gaussian Hilbert space L²(μ_Ψ) to the nuclear triple consisting of test functions' and distributions' spaces, (N)¹⊂ L²(μ_Ψ)⊂(N)_μΨ^-1. Furthermore, thanks to the definition of two transformations, S_μΨ and T_μΨ, we study Donsker's delta as an element within (N)_μΨ^-1 applying the integral equations fulfilled by _mΨ_q.

Cited by

• Generalized Wright Analysis: Stochastic and Applications
• A Generalization of the Fox H-function

Related

• Generalized Appell Systems
• Generalized Functions in Infinite Dimensional Analysis
• Small Sample Spaces for Gaussian Processes
• Measures on Hilbert-Schmidt operators and algebraic quantum field theory
• Operators on Spaces Generated by Infinite Dimensional Appell Polynomials