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![]() Title:Second Quantization and Evolution Operators in Infinite Dimension Conference:IMPMS 2026 Tags:Asymptotic Behavior, Evolution Operators, Hypercontractivity Property and Second Quantization Abstract: 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 $L^p(X,\gamma_t)$, $\{\gamma_t\}_{t\in R}$ 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. This is a joint work with Davide Addona (Università degli Studi di Parma). Second Quantization and Evolution Operators in Infinite Dimension ![]() Second Quantization and Evolution Operators in Infinite Dimension | ||||
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