# Singular spectrum of sturm-liouville operators under local perturbations

@article{Castillo1991SingularSO,
title={Singular spectrum of sturm-liouville operators under local perturbations},
author={Rafael Castillo},
journal={American Journal of Mathematics},
year={1991},
volume={113},
pages={203-217}
}
• R. Castillo
• Published 1 April 1991
• Mathematics
• American Journal of Mathematics
2 Citations

### Stability of a singular continuous spectrum of Sturm-Liouville operators

AbstractWe prove that there exists a continuous potentialq such that the operator generated by $$(lu)(x) = - u^n (x) + \{ q(x) + \upsilon (x)\} u(x), 0 \leqslant (x)< \infty$$ and boundary

### Embedded Eigenvalues of Sturm Liouville Operators

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,

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In general the potential function $q( x )$ in a Sturm–Liouville problem is uniquely determined by two spectra. It is shown here that if $q( x )$ is prescribed over the interval \$\left(

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Soit q=(α,β,q)∈(0,π) 2 ×L R 2 [0,1]. Le probleme de Sturm-Liouville −y''+q(x)y=λy, 0≤x≤1, y(0) cos α+y'(0) sin α=0; y(1) cos β+y(1) sin β=0, a un spectre discret de valeurs propres simples ν 0 (q)<ν

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01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. The interest in inverse problems of spectral analysis has increased considerably in recent