Second Quantization and Evolution Operators in infinite dimension

2025/02/12 by Addona, Davide, De Fazio, Paolo · 1 citation
#28C20 #34G10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2502.08572

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,γ_t), \γ_t\_t∈\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.

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• Stochastic and deterministic non-autonomous reaction-diffusion equations

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