Notes on Lieb-Thirring type inequality for a complex perturbation of fractional Schrödinger operator.

Clément Dubuisson (1)

1 IMB - Institut de Mathématiques de Bordeaux

For $s>0$, let $H_0=(-\Delta)^s$ be the fractional Laplacian. In this paper, we obtain Lieb-Thirring type inequalities for the fractional Schr\"odinger operator defined as $H=H_0+V$, where $V \in L^p(\mathbb{R}^d), p\ge 1, d\ge 1,$ is a complex-valued potential. Our methods are based on results of articles by Borichev-Golinskii-Kupin \cite{BoGoKu} and Hansmann \cite{Ha1}.

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

Domaines: Théorie spectrale [math.SP]

Clément Dubuisson. Notes on Lieb-Thirring type inequality for a complex perturbation of fractional Schrödinger operator.. 2015. ⟨hal-00959766v3⟩