On algebraic multiplicity of (Anti)periodic eigenvalues of hill?�s equations
Journal
Proceedings of the American Mathematical Society
Journal Volume
146
Journal Issue
7
Pages
3039-3047
Date Issued
2018
Author(s)
Chen, Z.
Abstract
We construct two explicit examples of Hill’s equations with complex-valued potentials such that the algebraic multiplicity of some (anti)periodic eigenvalue E equals 1 + 2pi with pi ≥ 1, where pi denotes the immovable part of E as a Dirichlet eigenvalue. These examples confirm a phenomena about Hill’s equations in (Gesztesy and Weikard, Acta Math. 176 (1996), 73–107).
Type
journal article