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Embedded eigenvalues of Sturm Liouville operators

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Abstract

In this work we study the behavior of embedded eigenvalues of Sturm-Liouville problems in the half axis under local perturbations. When the derivative of the spectral function is strictly positive, we prove that the embedded eigenvalues either disappear or remain fixed. In this case we show that local perturbations cannot add eigenvalues in the continuous spectrum. If the condition on the spectral function is removed then a local perturbation can add infinitely many eigenvalues.

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Authors and Affiliations

  1. IIMAS-UNAM, Admón No. 20, Delegación Alvaro Obregón, Apdo. Postal 20-726, 01000, México, D.F.

    Rafael R. del Río Castillo

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  1. Rafael R. del Río Castillo
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Communicated by B. Simon

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del Río Castillo, R.R. Embedded eigenvalues of Sturm Liouville operators. Commun.Math. Phys. 142, 421–431 (1991). https://doi.org/10.1007/BF02102068

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  • DOI: https://doi.org/10.1007/BF02102068

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