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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 105, 10 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.105 (Mi sigma1787) 		 
A Sharp Lieb–Thirring Inequality for Functional Difference Operators

Ari Laptevab, Lukas Schimmerc

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
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DOI: https://doi.org/10.3842/SIGMA.2021.105
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.
Funding agency Grant number
Russian Science Foundation 18-11-0032
Royal Swedish Academy of Sciences 2017-04736
A. Laptev was partially supported by RSF grant 18-11-0032. L. Schimmer was supported by VR grant 2017-04736 at the Royal Swedish Academy of Sciences.
Received: September 12, 2021; in final form November 25, 2021; Published online December 6, 2021
Bibliographic databases:
Document Type: Article
MSC: 47A75, 81Q10
Language: English
Citation: Ari Laptev, Lukas Schimmer, “A Sharp Lieb–Thirring Inequality for Functional Difference Operators”, SIGMA, 17 (2021), 105, 10 pp.
Citation in format AMSBIB
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\paper A Sharp Lieb--Thirring Inequality for Functional Difference Operators
\jour SIGMA
\yr 2021
\vol 17
\papernumber 105
\totalpages 10
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\crossref{https://doi.org/10.3842/SIGMA.2021.105}
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