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

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

Аннотация: 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.

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

MSC: 47A75, 81Q10

Поступила: 12 сентября 2021 г.; в окончательном варианте 25 ноября 2021 г.; опубликована 6 декабря 2021 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2021.105