Analysis & PDE
- Anal. PDE
- Volume 7, Number 6 (2014), 1397-1420.
On multiplicity bounds for Schrödinger eigenvalues on Riemannian surfaces
A classical result by Cheng in 1976, improved later by Besson and Nadirashvili, says that the multiplicities of the eigenvalues of the Schrödinger operator , where is -smooth, on a compact Riemannian surface are bounded in terms of the eigenvalue index and the genus of . We prove that these multiplicity bounds hold for an -potential , where . We also discuss similar multiplicity bounds for Laplace eigenvalues on singular Riemannian surfaces.
Anal. PDE, Volume 7, Number 6 (2014), 1397-1420.
Received: 19 November 2013
Revised: 5 May 2014
Accepted: 12 July 2014
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 58J50: Spectral problems; spectral geometry; scattering theory [See also 35Pxx] 35P99: None of the above, but in this section 35B05: Oscillation, zeros of solutions, mean value theorems, etc.
Kokarev, Gerasim. On multiplicity bounds for Schrödinger eigenvalues on Riemannian surfaces. Anal. PDE 7 (2014), no. 6, 1397--1420. doi:10.2140/apde.2014.7.1397. https://projecteuclid.org/euclid.apde/1513731587