Discontinuities cause essential spectrum

by Dr Giovanni Canestrari (University of Rome Tor Vergata)

Wednesday 9 Nov 2022, 15:00 → 16:00 Europe/Rome

Centro De Giorgi - SNS

In this seminar I will introduce transfer operators associated to piecewise monotone interval transformations and and show that, for a large class of Banach spaces, the essential spectrum is large whenever the transformation fails to be Markov.  After comparing our results with the literature, we show how to construct a family of Banach spaces which proves that the lower bound on the essential spectral radius is optimal. Indeed, these Banach spaces realize an essential spectral radius as close as desired to the theoretical best possible case.