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Improved Berezin—Li—Yau inequalities with magnetic field

Published online by Cambridge University Press:  30 January 2015

Hynek Kovařík  and
Timo Weidl
Hynek Kovařík
Affiliation:
Dipartimento di Matematica, Università degli studi di Brescia, Via Branze, 38-25123 Brescia, Italy, ([email protected])
Timo Weidl
Affiliation:
Institute of Analysis, Dynamics and Modelling, Universität Stuttgart, PF 80 11 40, 70569 Stuttgart, Germany, ([email protected])
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Abstract

In this paper we study the eigenvalue sums of Dirichlet Laplacians on bounded domains. Among our results we establish an improvement of the Berezin bound and of the Li—Yau bound in the presence of a constant magnetic field previously obtained by Erdős et al. and Melas.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 1 , February 2015 , pp. 145 - 160
Copyright
Copyright © Royal Society of Edinburgh 2015 

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