Spectral properties of Sturm-Liouville equations with singular energy-dependent potentials

2012/12/29 by Pronska, Nataliya
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1212.6671

Abstract

We study spectral properties of energy-dependent Sturm-Liouville equations, introduce the notion of norming constants and establish their interrelation with the spectra. One of the main tools is the linearization of the problem in a suitable Pontryagin space.

Related

• Asymptotics of eigenvalues and eigenfunctions of energy-dependent Sturm--Liouville equations
• Analyticity and uniform stability of the inverse singular\n Sturm--Liouville spectral problem
• Reconstruction of energy-dependent Sturm-Liouville equations from two\n spectra
• Recovering of a potential of Sturm-Liouville operator from a finite sets of eigenvalues and norming constants
• Inverse problems of spectral analysis for the Sturm-Liouville operator with regular boundary conditions