Laptev, AriAriLaptevSchimmer, LukasLukasSchimmer2022-01-132022-01-132021-12-06Symmetry, Integrability and Geometry: Methods and Applications, 2021, 17, pp.1-101815-0659http://hdl.handle.net/10044/1/93565We 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.© 2021 The Author(s).Science & TechnologyPhysical SciencesPhysics, MathematicalPhysicsLieb-Thirring inequalityfunctional difference operatorsemigroup propertyTOPOLOGICAL STRINGSBOUNDSJournal Articlehttps://www.dx.doi.org/10.3842/SIGMA.2021.105https://www.emis.de/journals/SIGMA/2021/105/