Abstract
We consider the Sturm-Liouville problem −y″ = λry on [−1, 1] with Dirichlet boundary conditions and with an indefinite weight function r which changes sign at 0. We discuss several conditions known to be either necessary or sufficient for the eigenfunctions to form a Riesz basis of the Hilbert space L 2,|r|(−1, 1). Assuming that the odd part of r dominates the even part in a certain sense, we show that the above conditions (and also some new ones) are in fact all equivalent to this Riesz basis property.
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© 2009 Birkhäuser Verlag Basel/Switzerland
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Binding, P., Fleige, A. (2009). Conditions for an Indefinite Sturm-Liouville Riesz Basis Property. In: Behrndt, J., Förster, KH., Trunk, C. (eds) Recent Advances in Operator Theory in Hilbert and Krein Spaces. Operator Theory: Advances and Applications, vol 198. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0180-1_6
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DOI: https://doi.org/10.1007/978-3-0346-0180-1_6
Publisher Name: Birkhäuser Basel
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