On algebraic multiplicity of (anti)periodic eigenvalues of Hill’s equations

Chen, Zhijie; Lin, Chang-Shou

doi:10.1090/proc/14003

On algebraic multiplicity of (anti)periodic eigenvalues of Hill’s equations
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Proc. Amer. Math. Soc. 146 (2018), 3039-3047 Request permission

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 $1+2p_{i}$ with $p_{i}\geq 1$, where $p_{i}$ 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).

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