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Corbinian Schlosser (LAAS-CNRS, Toulouse, France)
June 16, 2022 @ 13:00 - 14:00
Title: Koopman and Perron-Frobenius operators on reproducing kernel Hilbert spaces
Abstract: Koopman operators and reproducing kernel Hilbert spaces (RKHS) share a common idea: Giving linear representations of non-linear tasks or objects. We follow the recent path of combining both concepts. The Koopman operator is a composition operator and therefore acts on a function space – in this talk we consider the underlying function space to be an RKHS. We give an introduction to the Koopman operator on an RKHS as well as to its adjoint, the so-called Perron-Frobenius operator. Both operators are linear but not necessarily bounded. Thus we focus on elementary properties of these operators including closedness and boundedness. We present a collection of known and new results on Koopman operators on RKHS. These results, with no further specifications on the RKHS, are restrained and we emphasize that the RKHS should be chosen accordingly to the problem at hand in order to flourish the interplay between the Koopman operator and the RKHS.
The seminar will take place in room CH12 at the Faculty of Sciences