Ari Laptev, Lukas Schimmer, “A Sharp Lieb–Thirring Inequality for Functional Difference Operators”, SIGMA, 2021, Volume 17,105, 10 pp.

A Sharp Lieb–Thirring Inequality for Functional Difference Operators

Ari Laptev^ab, 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

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.

Keywords: Lieb–Thirring inequality, functional difference operator, semigroup property.

MSC: 47A75, 81Q10

Received: September 12, 2021; in final form November 25, 2021; Published online December 6, 2021

Language: English

DOI: 10.3842/SIGMA.2021.105