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

Authors: Zhijie Chen and Chang-Shou Lin
Journal: Proc. Amer. Math. Soc. 146 (2018), 3039-3047
MSC (2010): Primary 34B30
Published electronically: February 28, 2018
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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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Additional Information

Zhijie Chen
Affiliation: Department of Mathematical Sciences, Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, People’s Republic of China

Chang-Shou Lin
Affiliation: Taida Institute for Mathematical Sciences (TIMS), Center for Advanced Study in Theoretical Sciences (CASTS), National Taiwan University, Taipei 10617, Taiwan

Received by editor(s): July 9, 2017
Received by editor(s) in revised form: October 18, 2017
Published electronically: February 28, 2018
Additional Notes: The research of the first author was supported by NSFC (No. 11701312).
Communicated by: Lei Ni
Article copyright: © Copyright 2018 American Mathematical Society

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