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

2025/01/22 by Antônio Sá Barreto, Yiran Wang, Barreto, Antônio Sá +1 · 1 citation
Mathematics · Computer Science · #Spectral Theory in Mathematical Physics #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2501.12606

Abstract

We study the asymptotic behavior of the counting function of negative eigenvalues of Schrödinger operators with real valued potentials on asymptotically hyperbolic manifolds. We establish conditions on 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 (-∞,-E) as E→ 0.

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