One-dimensional interpolation inequalities, Carlson--Landau inequalities and magnetic Schrodinger operators
Alexei Ilyin, Ari Laptev, Michael Loss, Sergey Zelik
TL;DR
This paper develops refined interpolation inequalities for periodic functions, applies them to Carlson--Landau inequalities and magnetic Schrödinger operators, and derives Lieb-Thirring inequalities for these operators in multi-dimensional settings.
Contribution
It introduces new refined inequalities for periodic functions and extends Lieb-Thirring bounds to magnetic Schrödinger operators on cylinders.
Findings
Refined first-order interpolation inequalities for periodic functions
Enhanced Carlson--Landau-type inequalities
Lieb-Thirring inequalities for magnetic Schrödinger operators on cylinders
Abstract
In this paper we prove refined first-order interpolation inequalities for periodic functions and give applications to various refinements of the Carlson--Landau-type inequalities and to magnetic Schrodinger operators. We also obtain Lieb-Thirring inequalities for magnetic Schrodinger operators on multi-dimensional cylinders.
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Taxonomy
TopicsNumerical methods in inverse problems · Spectral Theory in Mathematical Physics · Advanced Mathematical Modeling in Engineering