Ornstein-Uhlenbeck semigroups in infinite dimension
Alessandra Lunardi, Diego Pallara
TL;DR
This survey paper reviews Ornstein-Uhlenbeck semigroups across various infinite-dimensional spaces, discussing their properties, generators, and recent results in Hilbert and Banach spaces.
Contribution
It provides a comprehensive overview of Ornstein-Uhlenbeck semigroups in infinite dimensions, including new results in Banach spaces.
Findings
Classical OU semigroup in Wiener spaces analyzed
Extension to Hilbert spaces discussed
Recent results for OU semigroups in Banach spaces presented
Abstract
This is a survey paper about Ornstein-Uhlenbeck semigroups in infinite dimension, and their generators. We start from the classical Ornstein-Uhlenbeck semigroup in Wiener spaces and then discuss the general case in Hilbert spaces. Finally, we present some results for O-U semigroups in Banach spaces.
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