On the eigenvalues of operators with gaps. Application to Dirac operators.

By Jean Dolbeault, Maria J. Esteban, É. Séré. 2000

154 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8322fe4a5ddf8cd71485cde3b90872ef9b60e53a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

From atoms to crystals: a mathematical journey (2005, background): “Another very interesting (see [86]) minimax characterization for λk is provided by (3.”
Variational methods in relativistic quantum mechanics (2007, background): “Actually, under the conditions (49)-(50)-(51), it can be seen that Dc + V has an infinite sequence of eigenvalues {λk(V )}k≥1 converging to 1, and it was proved in [51] that each of them can be obtained by a min-max procedure:”
Estimates for the optimal constants in multipolar Hardy inequalities for Schrödinger and Dirac operators (2008, background): “Under appropriate conditions, see [13, 14],”