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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 | References | Similar Articles | Additional Information

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 }$.


References [Enhancements On Off] (What's this?)

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Additional Information

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

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