A Sharp Lieb-Thirring Inequality for Functional Difference Operators

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• ISSN: 1815-0659
• Main Authors: Laptev, Ari, Schimmer, Lukas
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211422
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A Sharp Lieb-Thirring Inequality for Functional Difference Operators. Ari Laptev and Lukas Schimmer. SIGMA 17 (2021), 105, 10 pages

We prove sharp Lieb-Thirring type inequalities for the eigenvalues of a class of one-dimensional functional difference operators associated with mirror curves. We furthermore prove that the bottom of the essential spectrum of these operators is a resonance state.