In an infinite dimensional separable Hilbert space X, we study compactness and hypercontractivity properties of the Ornstein-Uhlenbeck evolution operators Ps,t in the spaces Lp(X,γt)[jls-end-space/], where {γt}t∈R being a suitable evolution system of measures for Ps,t[jls-end-space/]. Moreover, we study the asymptotic behavior of Ps,t[jls-end-space/]. Our results are obtained via 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.
Second quantization and evolution operators in infinite dimension / Addona, D., De Fazio, P.. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 291:9(2026). [10.1016/j.jfa.2026.111598]
Second quantization and evolution operators in infinite dimension
Addona D.
;De Fazio P.
2026-01-01
Abstract
In an infinite dimensional separable Hilbert space X, we study compactness and hypercontractivity properties of the Ornstein-Uhlenbeck evolution operators Ps,t in the spaces Lp(X,γt)[jls-end-space/], where {γt}t∈R being a suitable evolution system of measures for Ps,t[jls-end-space/]. Moreover, we study the asymptotic behavior of Ps,t[jls-end-space/]. Our results are obtained via 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
