Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 105, 10 pages      arXiv:2109.05465      https://doi.org/10.3842/SIGMA.2021.105
Contribution to the Special Issue on Mathematics of Integrable Systems: Classical and Quantum in honor of Leon Takhtajan

A Sharp Lieb-Thirring Inequality for Functional Difference Operators

Ari Laptev a and Lukas Schimmer c
a) Department of Mathematics, Imperial College London, London SW7 2AZ, UK
b) Saint Petersburg State University, Saint Petersburg, Russia
c) Institut Mittag-Leffler, The Royal Swedish Academy of Sciences, 182 60 Djursholm, Sweden

Received September 12, 2021, in final form November 25, 2021; Published online December 06, 2021

Abstract
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.

Key words: Lieb-Thirring inequality; functional difference operator; semigroup property.

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