Semiclassical Spectral Estimates with Renainder Terms

Series: 
Math Physics Seminar
Friday, November 17, 2017 - 15:00
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
Univ. Stuttgart
,  

This is part of the 2017 Quolloquium series.

Starting from the classical Berezin- and Li-Yau-bounds onthe eigenvalues of the Laplace operator with Dirichlet boundaryconditions I give a survey on various improvements of theseinequalities by remainder terms. Beside the Melas inequalitywe deal with modifications thereof for operators with and withoutmagnetic field and give bounds with (almost) classical remainders.Finally we extend these results to the Heisenberg sub-Laplacianand the Stark operator in domains.