The Riesz Basis Property of an Indefinite Sturm-Liouville Problem with a Non-Odd Weight Function |
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Authors: | Andreas Fleige |
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Institution: | (1) Baroper Schulstrasse 27a, D-44225 Dortmund, Germany |
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Abstract: | For the Sturm-Liouville eigenvalue problem − f′′ = λrf on −1, 1] with Dirichlet boundary conditions and with an indefinite weight function r changing its sign at 0 we discuss the question whether the eigenfunctions form a Riesz basis of the Hilbert space L
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|r|− 1, 1]. So far a number of sufficient conditions on r for the Riesz basis property are known. However, a sufficient and necessary condition is only known in the special case of
an odd weight function r. We shall here give a generalization of this sufficient and necessary condition for certain generally non-odd weight functions
satisfying an additional assumption.
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Keywords: | Primary 34B4 Secondary 34L10 |
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