BCAM Working Seminar APDE: Construction of quasimodes for non-selfadjoint operators using propagation of wave-packets

Abstract
In this talk, I will present new results on the study of pseudospectra of non-selfadjoint operators. As it is well known, the precise knowledge of the high-energy distribution of the spectrum of a non-selfadjoint Schrödinger operator is not always enough to obtain proper estimates on the resolvent (contrary to the self-adjoint case), which is essential, for instance, to obtain optimal decay rates for the energy of solutions to the evolution problem governed by such an operator. A more suitable object of study in this framework is the pseudo-spectrum, given by the set of points in the complex plane for which it is possible to find an approximate solution to the eigenvalue problem (which are not necessarily asymptotically close to true eigenvalues). Using recent developments on the description of the propagation of Hagedorn wave-packets by non-Hermitian quadratic operators, we give new constructions of quasimodes which test resolvent estimates for certain semiclassical non-selfadjoint operators satisfying suitable dynamical assumptions.

Link to the session: https://zoom.us/j/95050577455?pwd=cCtVSnFTd2JKTDVhSEQ0UmNZWTBLQT09