Work

The distribution of negative eigenvalues of Schrödinger operators on asymptotically hyperbolic manifolds

Year: 2025

Type: article

Abstract: We study the asymptotic behavior of the counting function of negative eigenvalues of Schrödinger operators with real valued potentials which decay at infinity on asymptotically hyperbolic manifolds. We establish conditions on the rate of decay of the potential that determine if there are finitely or infinitely many negative eigenvalues. In the latter case, they may only accumulate at zero and we obtain the asymptotic behavior of the counting function of eigenvalues in an interval (-\infty, -E) as E\rightarrow 0 .

Source: Journal of Spectral Theory

DOI: 10.4171/jst/561

Authors: Antônio Sá Barreto, Yiran Wang

Institutions: Purdue University West Lafayette, Emory University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Award: Space-Time Structure Reconstruction in Cosmology and Lorentzian Geometry