Riesz Bases of Root Vectors of Indefinite Sturm-Liouville Problems with Eigenparameter Dependent Boundary Conditions. II

Binding, Paul; Ćurgus, Branko

doi:10.1007/s00020-009-1659-0

Cited by 5 publications

(1 citation statement)

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“…The relevant results from [30] are reviewed in Section 4.1. We note that the methods of [12] were used in [6] to give sufficient conditions for the Riesz basis property of problem (1.1) subject to linear self-adjoint λ-dependent boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

The Riesz basis property of an indefinite Sturm-Liouville problem with non-separated boundary conditions

Ćurgus,

Fleige,

Kostenko

2013

Preprint

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We consider a regular indefinite Sturm-Liouville eigenvalue problem −f ′′ + qf = λrf on [a, b] subject to general self-adjoint boundary conditions and with a weight function r which changes its sign at finitely many, so-called turning points. We give sufficient and in some cases necessary and sufficient conditions for the Riesz basis property of this eigenvalue problem. In the case of separated boundary conditions we extend the class of weight functions r for which the Riesz basis property can be completely characterized in terms of the local behavior of r in a neighborhood of the turning points. We identify a class of non-separated boundary conditions for which, in addition to the local behavior of r in a neighborhood of the turning points, local conditions on r near the boundary are needed for the Riesz basis property. As an application, it is shown that the Riesz basis property for the periodic boundary conditions is closely related to a regular HELP-type inequality without boundary conditions.

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Section: Introductionmentioning

confidence: 99%