The spectrum of Schrödinger operators with positive potentials in Riemannian manifolds

DOI10.1090/S0002-9939-03-06968-5zbMath1057.58016OpenAlexW1533474269WikidataQ115290163 ScholiaQ115290163MaRDI QIDQ4417245

Zhongwei Shen

Publication date: 28 July 2003

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-03-06968-5

zbMATH Keywords

Schrödinger operatorRiemannian manifolddiscrete spectrum

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Schrödinger operator, Schrödinger equation (35J10)

Related Items (7)

A spectral property of discrete Schrödinger operators with non-negative potentials ⋮ Fractional square functions and potential spaces. II ⋮ Coulomb systems on Riemannian manifolds and stability of matter ⋮ The spectral bounds of the discrete Schrödinger operator ⋮ Behaviour of heat kernels of Schrödinger operators and applications to certain semilinear parabolic equations ⋮ A characterization related to Schrödinger equations on Riemannian manifolds ⋮ On the essential spectrum of Schrödinger operators on Riemannian manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Schrödinger equation and the eigenvalue problem
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Exponential stability of a diffusion equation with absorption
• The Rozenblum-Lieb-Cwikel inequality for Markov generators
• The spectral bound and principal eigenvalues of Schrödinger operators on Riemannian manifolds
• \(L^ p\) estimates for Schrödinger operators with certain potentials
• On bounds of \(N(\lambda)\) for a magnetic Schrödinger operator
• The uncertainty principle
• Eigenvalue asymptotics and exponential decay of eigenfunctions for Schrödinger operators with magnetic fields
• A note on the isoperimetric constant

This page was built for publication: The spectrum of Schrödinger operators with positive potentials in Riemannian manifolds