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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Multiplicities of the eigenvalues of the discrete Schrödinger equation in any dimension


Authors: Dan Burghelea and Thomas Kappeler
Journal: Proc. Amer. Math. Soc. 102 (1988), 255-260
MSC: Primary 15A18,; Secondary 39A12
DOI: https://doi.org/10.1090/S0002-9939-1988-0920982-3
MathSciNet review: 920982
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Abstract: The following von Neumann-Wigner type result is proved: The set of potentials $ a:\;\Gamma \to {\mathbf{R}}(\Gamma \subseteq {{\mathbf{Z}}^N})$, with the property that the corresponding discrete Schrödinger equation $ {\Delta _d} + a$ has multiple eigenvalues when considered with certain boundary conditions, is an algebraic set of $ {\text{codimension}} \geq {\text{2}}$ within $ {{\mathbf{R}}^\Gamma }$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0920982-3
Article copyright: © Copyright 1988 American Mathematical Society