4 citations · 10 across the 7 of their papers we have counts for
10 papers
Eigenvalues of non-selfadjoint functional difference operators
Alexei Ilyin, Ari Laptev, Lukas Schimmer +1
Using the well known approach developed in the papers of B. Davies and his co-authors we obtain inequalities for the location of possible complex eigenvalues of non-selfadjoint fun…
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…
Calogero type bounds in two dimensions
Ari Laptev, Larry Read, Lukas Schimmer
For a Schrödinger operator on the plane with electric potential and Aharonov--Bohm magnetic field we obtain an upper bound on the number of its negative eigenval…
A Sharp Lieb-Thirring Inequality for Functional Difference Operators
Ari Laptev, Lukas Schimmer
We prove sharp Lieb-Thirring type inequalities for the eigenvalues of a class of one-dimensional functional difference operators associated to mirror curves. We furthermore prove t…
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…
Improved sharp spectral inequalities for Schrödinger operators on the semi-axis
Lukas Schimmer
We prove a Lieb--Thirring inequality for Schrödinger operators on the semi-axis with Robin boundary condition at the origin. The result impr…
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…
Endpoint resolvent estimates for compact Riemannian manifolds
Rupert L. Frank, Lukas Schimmer
We prove bounds for the resolvent of the Laplace-Beltrami operator on a compact Riemannian manifold of dimension in the endpoint case . It has t…
Weyl type asymptotics and bounds for the eigenvalues of functional-difference operators for mirror curves
Ari Laptev, Lukas Schimmer, Leon A. Takhtajan
We investigate Weyl type asymptotics of functional-difference operators associated to mirror curves of special del Pezzo Calabi-Yau threefolds. These operators are $H(ζ)=U+U^{-1}+V…
Spectral inequalities for Jacobi operators and related sharp Lieb-Thirring inequalities on the continuum
Lukas Schimmer
In this paper we approximate a Schrödinger operator on by Jacobi operators on to provide new proofs of sharp Lieb-Thirring inequalities for the powers $γ=1/2…