Green's Functions and Spectral Theory for the Hill's Equation

2015/11/03 by Alberto Cabada, Cabada, Alberto, José A. Cid +3
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1511.00899

arxiv created 2015/11/03 · arxiv updated 2015/11/04

Abstract

The aim of this paper is to show certain properties of the Green's functions related to the Hill's equation coupled with different two point boundary value conditions. We will obtain the expression of the Green's function of Neumann, Dirichlet, Mixed and anti-periodic problems as a combination of the Green's function related to periodic ones. As a consequence we will prove suitable results in spectral theory and deduce some comparison results for the solutions of the Hill's equation with different boundary value conditions.

Related

• Relationship of the Green's functions related to the Hill's equation coupled to different boundary value conditions
• Green's functions for even order boundary value problems
• Algorithms for estimating spectral density functions for periodic\n potentials on the half line
• About one inverse problem for a Hill's equation with double eigenvalues
• Solutions and Green's function of the first order linear equation with reflection and initial conditions