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2014 On multiplicity bounds for Schrödinger eigenvalues on Riemannian surfaces
Gerasim Kokarev
Anal. PDE 7(6): 1397-1420 (2014). DOI: 10.2140/apde.2014.7.1397

Abstract

A classical result by Cheng in 1976, improved later by Besson and Nadirashvili, says that the multiplicities of the eigenvalues of the Schrödinger operator (Δg+ν), where ν is C-smooth, on a compact Riemannian surface M are bounded in terms of the eigenvalue index and the genus of M. We prove that these multiplicity bounds hold for an Lp-potential ν, where p>1. We also discuss similar multiplicity bounds for Laplace eigenvalues on singular Riemannian surfaces.

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Gerasim Kokarev. "On multiplicity bounds for Schrödinger eigenvalues on Riemannian surfaces." Anal. PDE 7 (6) 1397 - 1420, 2014. https://doi.org/10.2140/apde.2014.7.1397

Information

Received: 19 November 2013; Revised: 5 May 2014; Accepted: 12 July 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1301.58016
MathSciNet: MR3270168
Digital Object Identifier: 10.2140/apde.2014.7.1397

Subjects:
Primary: 35B05 , 35P99 , 58J50

Keywords: eigenvalue multiplicity , nodal set , Riemannian surface , Schrödinger equation

Rights: Copyright © 2014 Mathematical Sciences Publishers

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