Vorträge in der Woche 08.10.2018 bis 14.10.2018

Dienstag, 09.10.2018: Flow Semigroups and Superstability

Logan Hart (Baton Rouge)

My talk will be based on preliminary work done in the dissertation of Austin Scirratt (LSU 2016). I will try to characterize the “superstability” of a semigroup Exp[tA] in terms of spectral properties of the generator A, where “superstability” means that Exp[tA] decays “faster than any exponential” towards zero as time t tends to infinity. In particular, I will answer an open question of A. V. Balakrishnan from 2005 by providing elementary physical examples of superstability which are not of the type of extinction-in-finite-time (i.e., not nilpotent) and are less artificial (in the context of semigroup theory) than those given by G. Lumer in 2002.