Speaker: Isao Ishikawa, Ehime University

Date: September 22, 2022

Abstract: We investigate the boundedness of weighted Koopman operators defined on a quasi-Banach space continuously included in the space of smooth functions on a manifold. We prove that the boundedness of weighted Koopman operators strongly limits the behavior of the original map, and it provides us with an effective method to investigate the properties of Koopman operators via the theory of dynamical systems. As a result, we prove that only affine maps can induce a bounded weighted Koopman operator with non-vanishing weight on any infinite-dimensional quasi-Banach space continuously included in the space of entire functions on the complex plane. We also prove any polynomial automorphisms except affine transforms cannot induce a bounded weighted Koopman operator on a quasi-Banach space composed of entire functions in the two-dimensional complex affine space under conditions.

Slides