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Hardy-type estimates for Dirac operators

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Date
2007
Link to item file
http://hal.archives-ouvertes.fr/hal-00112858/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
Hardy inequality; Dirac operator; Coulomb potential; Optimal constants; Dirac-Coulomb Hamiltonian; relativistic Hydrogen atom
Journal issue
Annales Scientifiques de l'École Normale Supérieure
Volume
40
Number
6
Publication date
2007
Article pages
885-900
URI
https://basepub.dauphine.fr/handle/123456789/701
Collections
  • CEREMADE : Publications
Metadata
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Author
Dolbeault, Jean
Duoandikoetxea, Javier
Esteban, Maria J.
Vega, Luis
Type
Article accepté pour publication ou publié
Abstract (EN)
We prove some Hardy type inequalities related to the Dirac operator by elementary methods, for a large class of potentials, which even includes measure valued potentials. Optimality is achieved by the Coulomb potential. When potentials are smooth enough, our estimates provide some spectral information on the operator.

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