On quantitative bounds on eigenvalues of a complex perturbation of a Dirac operator

Clément Dubuisson (1)

1 IMB - Institut de Mathématiques de Bordeaux

We prove a Lieb-Thirring type inequality for a complex perturbation of a d-dimensional massive Dirac operator $D_m, m\geq 0$ whose spectrum is $]-\infty , -m]\cup[m , +\infty[$. The difficulty of the study is that the unperturbed operator is not bounded from below in this case, and, to overcome it, we use the methods of complex function theory. The methods of the article also give similar results for complex perturbations of the Klein-Gordon operator.

Mots clés: Dirac operator; complex perturbation; discrete spectrum; Lieb-Thirring type inequality; conformal mapping; perturbation determinant

Domaines: Théorie spectrale [math.SP]

Clément Dubuisson. On quantitative bounds on eigenvalues of a complex perturbation of a Dirac operator. Integral Equations and Operator Theory, 2014, 78 (2), pp.249-269. ⟨10.1007/s00020-013-2112-y⟩. ⟨hal-00825047v4⟩