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An analytical proof of Hardy-like inequalities related to the Dirac operator

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Nov 2004Embargo end date: 01 Jan 2003 France English Publisher:Elsevier BVJournal:Journal of Functional Analysis, volume 216, pages 1-21 (issn: 0022-1236,

Authors: Loss, Michael; Esteban, Maria J.; Dolbeault, Jean; Vega, Luis;

doi: 10.1016/j.jfa.2003.09.010 , 10.48550/arxiv.math-ph/0309065

arXiv: http://arxiv.org/abs/math-ph/0309065

An analytical proof of Hardy-like inequalities related to the Dirac operator

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Abstract

We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.

LaTex, 22 pages

Country

France

Related Organizations

Paris Dauphine University
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Keywords

Dirac–Coulomb Hamiltonian, Dirac operator, Dirac-Coulomb Hamiltonian, FOS: Physical sciences, PDEs in connection with relativity and gravitational theory, sharp Hardy-type inequalities, Mathematical Physics (math-ph), Analyse, 510, 004, Optimal constants, Relativistic Hydrogen atom, uncertainty principle, Applications of functional analysis in quantum physics, 515, Hardy inequality, 35Q40, 35Q75, 46N50, 81Q10, Analysis, Mathematical Physics, PDEs in connection with quantum mechanics, Selfadjoint operator theory in quantum theory, including spectral analysis

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NSF| Dynamics and Variational Problems