Generalized Wright Analysis in Infinite Dimensions
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916862518886400 |
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| author | Beghin, Luisa Cristofaro, Lorenzo da Silva, José L. |
| author_facet | Beghin, Luisa Cristofaro, Lorenzo da Silva, José L. |
| contents | 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 $\mathbb{R}^d$, then define them in an abstract nuclear triple $\mathcal{N}\subset\mathcal{H}\subset\mathcal{N}'$. 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 $L^2(μ_Ψ)$ to the nuclear triple consisting of test functions' and distributions' spaces, $(\mathcal{N})^{1}\subset L^2(μ_Ψ)\subset(\mathcal{N})_{μ_Ψ}^{-1}$. Furthermore, thanks to the definition of two transformations, $S_{μ_Ψ}$ and $T_{μ_Ψ}$, we study Donsker's delta as an element within $(\mathcal{N})_{μ_Ψ}^{-1}$ applying the integral equations fulfilled by $_mΨ_q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01665 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Wright Analysis in Infinite Dimensions Beghin, Luisa Cristofaro, Lorenzo da Silva, José L. Probability Functional Analysis 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 $\mathbb{R}^d$, then define them in an abstract nuclear triple $\mathcal{N}\subset\mathcal{H}\subset\mathcal{N}'$. 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 $L^2(μ_Ψ)$ to the nuclear triple consisting of test functions' and distributions' spaces, $(\mathcal{N})^{1}\subset L^2(μ_Ψ)\subset(\mathcal{N})_{μ_Ψ}^{-1}$. Furthermore, thanks to the definition of two transformations, $S_{μ_Ψ}$ and $T_{μ_Ψ}$, we study Donsker's delta as an element within $(\mathcal{N})_{μ_Ψ}^{-1}$ applying the integral equations fulfilled by $_mΨ_q$. |
| title | Generalized Wright Analysis in Infinite Dimensions |
| topic | Probability Functional Analysis |
| url | https://arxiv.org/abs/2405.01665 |