QLunch: Lukas Schimmer

Speaker: Lukas Schimmer, The Royal Swedish Academy of Sciences

Title: Improved spectral inequalities for Jacobi operators as conjectured by Hundertmark and Simon

Abstract: In connection with their famous 1975 paper on the stability of matter in quantum mechanics, Lieb and Thirring developed a family of spectral inequalities for Schrödinger operators. In 2002, Hundertmark and Simon proved similar inequalities for Jacobi operators. They conjectured that their bounds could be improved by replacing a term (which depends on the off-diagonal parts of the operator) by its positive part. In this talk, I will present a proof of their conjecture. The key ingredient is to employ an additional convexity argument. I will also show how an argument in the original proof can be replaced by using a convolution property of the resolvent kernels.