Seminario: “Continuous and holomorphic semicocycles in Banach spaces”

Giovedì 5 Aprile 2018, ore 15:30 - Sala Riunioni VII Piano - Mark Elin


Giovedì 5 Aprile 2018 alle ore 15:30 in Sala Riunioni VII Piano, Mark Elin (ORT Braude College, Israele) terrà un seminario dal titolo “Continuous and holomorphic semicocycles in Banach spaces”.

Semicocycles appear naturally in the study of the asymptotic behavior of non-autonomous differential equations. They play an important role in the theory of dynamical systems and are closely connected to semigroups of weighted composition operators. In this talk, we consider semicocycles whose elements are either continuous or holomorphic mappings on a domain in a real/complex Banach space and take values in a unital Banach algebra.
We study semicocycle properties employing, in particular, their link with (non-linear) semigroups. On the other hand, we discover a dissimilarity of these two classes. We establish, in particular, conditions for the differentiability of a semicocycle.
Simplest semicocycles are those independent of the spatial variable. So, the problem (called the linearization problem) is to establish whether a semicocycle is cohomologous to such independent one.
Focusing on the linearization problem, we provide some criteria for a semicocycle to be linearizable as well as several easily verifiable sufficient conditions. These conditions are essential even for semicocycles over linear semigroups.
The talk is based on joint work with F. Jacobzon and G. Katriel.