Mathematical Physics and Harmonic Analysis Seminar

Date: October 6, 2021

Time: 10:00AM - 11:00AM

Location: Zoom

Speaker: Ivan Veselic, Dortmund (Germany)

Title: Scale free unique continuation estimates and applications for periodic and random operators

Abstract: With Ivica Nakic, Matthias Taeufer and Martin Tautenhahn we established a quantitative unique continuation estimate for spectral projectors of Schroedinger operators. It compares the L^2 norm of a function in a spectral subspace associated to a bounded energy interval to the L^2 norm on an equidistributed set. These estimates allow to give quantitative two-sided bounds on the lifting of edges of bands of essential spectrum, as well as on discrete eigenvalues between two such bands. It also allows to deduce Anderson localization in regimes where this was not possible before. For instance, Albrecht Seelmann and Matthias Taeufer showed that Anderson localization occurs at random perturbations of band edges of periodic potentials, whether the edges exhibit regular Floquet eigenvalue minima or not.