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.Mathematics Subject Classification (2000)Primary 34B09, 34B24Secondary 34L10KeywordsIndefinite Sturm-Liouville problemRiesz basis
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