3 papers
math-ph2022
The state of the Lieb--Thirring conjecture
Lukas Schimmer
In 1976 Lieb and Thirring established upper bounds on sums of powers of the negative eigenvalues of a Schrödinger operator in terms of semiclassical phase-space integrals. Over the…
math.CA2020
A remark on a paper by Hundertmark and Simon
Ari Laptev, Michael Loss, Lukas Schimmer
We prove a sharp Lieb-Thirring type inequality for Jacobi matrices, thereby settling a conjecture of Hundertmark and Simon. An interesting feature of the proof is that it employs a…
math-ph2018
Friedrichs Extension and Min-Max Principle for Operators with a Gap
Lukas Schimmer, Jan Philip Solovej, Sabiha Tokus
Semibounded symmetric operators have a distinguished self-adjoint extension, the Friedrichs extension. The eigenvalues of the Friedrichs extension are given by a variational princi…