Second Quantization and Evolution Operators in infinite dimension
Abstract
In an infinite dimensional separable Hilbert space X, we study compactness properties and the hypercontractivity of the Ornstein-Uhlenbeck evolution operators Ps,t in the spaces Lp(X,γt), \γt\t∈ being a suitable evolution system of measures for Ps,t. Moreover, we study the asymptotic behavior of Ps,t. Our results are produced thanks to a representation formula for Ps,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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