Open AccessOn algebraic multiplicity of (anti)periodic eigenvalues of Hill’s equations
Author(s) -
Zhijie Chen,
Chang–Shou Lin
Publication year - 2018
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/14003
Subject(s) - algorithm , annotation , computer science , artificial intelligence
We construct two explicit examples of Hill’s equations with complex-valued potentials such that the algebraic multiplicity of some (anti)periodic eigenvalue E E equals 1 + 2 p i 1+2p_{i} with p i ≥ 1 p_{i}\geq 1 , where p i p_{i} denotes the immovable part of E E as a Dirichlet eigenvalue. These examples confirm a phenomena about Hill’s equations in (Gesztesy and Weikard, Acta Math. 176 (1996), 73–107).