From Operators and Function Theory to Parabolic Problems: Semigroups everywhere

17.01.2018, 14:00 Uhr  –  Haus 9, Raum 2.22
Institutskolloquium

Wolfgang Arendt (Universität Ulm), Isabelle Chalendar (University Paris Est)

The colloquium begins at 14:00  with a talk

Composition operators on spaces of analytic functions: universality and asymptotics

by Isabelle Chalendar (University Paris Est)

Abstract:
Composition operators, namely linear operators acting on a space of holomorphic functions obtained by composing with a fixed function, have attracted attention for many years. One reason is the interesting interplay between the theory of holomorphic functions and operator theory, another is the universal character of composition operators.
One operator theoretical topic which seems to be neglected so far is the asymp-totic behaviour of the powers Tn of a composition operator T. This is the sub-ject of this talk, where we will also give an outlook on semigroups of composi-tion operators induced by analytic semiflows.

At 15:00 there will be a coffee break followed by the second talk

One-parameter semigroups: spectrum and asymptotics

by Wolfgang Arendt (University of Ulm)

Abstract:
Einar Hille's monograph "Functional Analysis and Semigroups" came out 70 years ago and with it were born the foundations of a theory which has since then seen a spectacular development.
We will give an overview concentrating on spectral theory and asymptotic behav-iour with emphasis on positive semigroups (Perron Frobenius Semigroups). Here kernels, irreducibility and principal eigenvalues play a particular role. Applications are given to new results on parabolic problems with diverse boundary conditions.