Corpus ID: 237494719

# A sharp Lieb--Thirring inequality for functional difference operators

@inproceedings{Laptev2021ASL,
title={A sharp Lieb--Thirring inequality for functional difference operators},
author={A. Laptev and L. Schimmer},
year={2021}
}
• Published 2021
• Mathematics, Physics
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 that the bottom of the essential spectrum of these operators is a resonance state. To our friend and coauthor Leon Takhtajan on the occasion of his 70th birthday

#### References

SHOWING 1-10 OF 18 REFERENCES
A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator
• Mathematics, Physics
• 1998
We give a proof of the Lieb-Thirring inequality in the critical case d=1, γ = 1/2, which yields the best possible constant.
New bounds on the Lieb-Thirring constants
• Mathematics, Physics
• 2000
Abstract.Improved estimates on the constants Lγ,d, for 1/2<γ<3/2, d∈N, in the inequalities for the eigenvalue moments of Schrödinger operators are established.
The spectral theory of a functional-difference operator in conformal field theory
• Mathematics
• 2015
We consider the functional-difference operator , where and are the Weyl self-adjoint operators satisfying the relation , , . The operator has applications in the conformal field theory andExpand
Liouville model on the lattice
• Physics
• 1988
Liouville equation is put on the lattice in a completely integrable way. The classical version is investigated in details and a lattice deformation of the Virasoro algebra is obtained. The quantumExpand
Operators from Mirror Curves and the Quantum Dilogarithm
• Mathematics, Physics
• 2015
Mirror manifolds to toric Calabi–Yau threefolds are encoded in algebraic curves. The quantization of these curves leads naturally to quantum-mechanical operators on the real line. We show that, for aExpand
Lieb-Thirring Inequalities for Jacobi Matrices
• Mathematics, Computer Science
• J. Approx. Theory
• 2002
For a Jacobi matrix J on ?2(Z+) with Ju(n)=an?1u(n?1)+bnu( n)+anu(n+1), it is proved that E2(E2?4)1/2??n?bn?+4?n?an-1? and bounds on higher moments are proved. Expand
Exact solutions to quantum spectral curves by topological string theory
• Physics
• 2015
A bstractWe generalize the conjectured connection between quantum spectral problems and topological strings to many local almost del Pezzo surfaces with arbitrary mass parameters. The conjecture usesExpand
Matrix Models from Operators and Topological Strings, 2
• Physics, Mathematics
• 2016
The quantization of mirror curves to toric Calabi–Yau threefolds leads to trace class operators, and it has been conjectured that the spectral properties of these operators provide a non-perturbativeExpand
The Quantum Dilogarithm and Dehn Twists in Quantum TeichmÜller Theory
By using the remarkable properties of the (non-compact) quantum dilogarithm it is shown that the Dehn twist operator in quantum Teichmuller theory has a complete continuous spectrum, the eigenvectorsExpand
Weyl Type Asymptotics and Bounds for the Eigenvalues of Functional-Difference Operators for Mirror Curves
• Mathematics, Physics
• 2015
We investigate Weyl type asymptotics of functional-difference operators associated to mirror curves of special del Pezzo Calabi-Yau threefolds. These operators are {H(\zeta) = U + U^{-1} + V +Expand