On the Eigenvalues of Operators with Gaps. Application to Dirac Operators

Dolbeault, Jean; Esteban, Maria J.; Séré, Eric

Dolbeault, Jean; Esteban, Maria J.; Séré, Eric (2000), On the Eigenvalues of Operators with Gaps. Application to Dirac Operators, Journal of Functional Analysis, 174, 1, p. 208-226. http://dx.doi.org/10.1006/jfan.1999.3542

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Type

Article accepté pour publication ou publié

Date

2000

Journal name

Journal of Functional Analysis

Volume

174

Number

Publisher

Elsevier

Pages

208-226

Abstract (EN)

This paper is devoted to a general min-max characterization of the eigenvalues in a gap of the essential spectrum of a self-adjoint unbounded operator. We prove an abstract theorem, then we apply it to the case of Dirac operators with a Coulomb-like potential. The result is optimal for the Coulomb potential.

Subjects / Keywords

variational methods; self-adjoint operators; quadratic forms; spectral gaps; eigenvalues; min-max; Rayleigh–Ritz quotients; Dirac operators; Hardy's inequality