Work

Bounds for eigenvalue sums of Schrödinger operators with complex radial potentials

Year: 2025

Type: article

Abstract: We consider eigenvalue sums of Schrödinger operators -\Delta+V on L^{2}(\R^{d}) with complex radial potentials V\in L^{q}(\mathbb{R}^{d}) , q . We prove quantitative bounds on the distribution of the eigenvalues in terms of the L^{q} norm of V . A consequence of our bounds is that, if the eigenvalues (z_{j}) accumulate to a point in (0,\infty) , then (\operatorname{Im}z_{j}) is summable. The key technical tools are resolvent estimates in Schatten spaces. We show that these resolvent estimates follow from spectral measure estimates by an epsilon removal argument.

Source: Journal of Spectral Theory

DOI: 10.4171/jst/576

Authors: Jean-Claude Cuenin, Solomon Keedle-Isack

Institution: Loughborough University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Loughborough University, Engineering and Physical Sciences Research Council

Award: Harmonic analysis techniques in spectral theory