Second Quantization and Evolution Operators in infinite dimension
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908300803571712 |
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| author | Addona, Davide De Fazio, Paolo |
| author_facet | Addona, Davide De Fazio, Paolo |
| contents | In an infinite dimensional separable Hilbert space $X$, we study compactness properties and the hypercontractivity of the Ornstein-Uhlenbeck evolution operators $P_{s,t}$ in the spaces $L^p(X,γ_t)$, $\{γ_t\}_{t\in\R}$ being a suitable evolution system of measures for $P_{s,t}$. Moreover, we study the asymptotic behavior of $P_{s,t}$. Our results are produced thanks to a representation formula for $P_{s,t}$ through the second quantization operator. Among the examples, we consider the transition evolution operator associated to a non-autonomous stochastic parabolic PDE. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08572 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Second Quantization and Evolution Operators in infinite dimension Addona, Davide De Fazio, Paolo Functional Analysis Analysis of PDEs 28C20, 34G10 In an infinite dimensional separable Hilbert space $X$, we study compactness properties and the hypercontractivity of the Ornstein-Uhlenbeck evolution operators $P_{s,t}$ in the spaces $L^p(X,γ_t)$, $\{γ_t\}_{t\in\R}$ being a suitable evolution system of measures for $P_{s,t}$. Moreover, we study the asymptotic behavior of $P_{s,t}$. Our results are produced thanks to a representation formula for $P_{s,t}$ through the second quantization operator. Among the examples, we consider the transition evolution operator associated to a non-autonomous stochastic parabolic PDE. |
| title | Second Quantization and Evolution Operators in infinite dimension |
| topic | Functional Analysis Analysis of PDEs 28C20, 34G10 |
| url | https://arxiv.org/abs/2502.08572 |