Abstract
For the Sturm-Liouville eigenvalue problem −f″ = γrf [−1, 1] with Dirichlet boundary conditions and with an indefinite weight function r changing it’s sign at 0 we discuss the question whether the eigenfunctions form a Riesz basis of the Hilbert space L 2|r| [−1, 1]. In the nineties the sufficient so called generalized one hand Beals condition was found for this Riesz basis property. Now using a new criterion of Parfyonov we show that already the old approach gives rise to a necessary and sufficient condition for the Riesz basis property under certain additional assumptions.
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© 2007 Birkhäuser Verlag Basel/Switzerland
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Fleige, A. (2007). A Necessary Aspect of the Generalized Beals Condition for the Riesz Basis Property of Indefinite Sturm-Liouville Problems. In: Förster, KH., Jonas, P., Langer, H., Trunk, C. (eds) Operator Theory in Inner Product Spaces. Operator Theory: Advances and Applications, vol 175. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8270-4_5
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DOI: https://doi.org/10.1007/978-3-7643-8270-4_5
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