6 papers
The sharp one-dimensional Lieb-Thirring inequality for the sum of eigenvalues
Larry Read, Marvin R. Schulz
We prove that the best constant in the one-dimensional Lieb-Thirring inequality with exponent one is , confirming the Lieb-Thirring conjecture in this case. Moreove…
Jost solutions and direct scattering for the continuum Calogero-Moser equation
Rupert L. Frank, Larry Read
We propose an inverse scattering transform for the continuum Calogero-Moser equation. We give a rigorous treatment of the direct scattering problem by constructing the associated J…
Sharp quantitative integral inequalities for harmonic extensions
Rupert L. Frank, Jonas W. Peteranderl, Larry Read
We prove a quantitative version of a sharp integral inequality by Hang, Wang, and Yan for both the Poisson operator and its adjoint. Our result has the strongest possible norm and…
Concentration of eigenfunctions on singular Riemannian manifolds
Charlotte Dietze, Larry Read
We consider a compact Riemannian manifold with boundary and a metric that is singular at the boundary. The associated Laplace-Beltrami operator is of the form of a Grushin operator…
On the asymptotic number of low-lying states in the two-dimensional confined Stark effect
Larry Read
We investigate the Stark operator restricted to a bounded domain with Dirichlet boundary conditions. In the semiclassical limit, a three-term asymptotic expa…
Negative spectrum of Schrödinger Operators with Rapidly Oscillating Potentials
Larry Read
For Schrödinger operators with potentials that are asymptotically homogeneous of degree , the size of the coupling determines whether it has finite or infinitely many negative…