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Moscow Mathematical Journal

Volume 15, Issue 3, July–September 2015  pp. 511–526.

On the Basis Property of the Root Functions of Sturm–Liouville Operators with General Regular Boundary Conditions

Authors:  Cemile Nur and O. A. Veliev
Author institution:Department of Mathematics, Dogus University, Kadikӧy, Istanbul, Turkey


We obtain the asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm–Liouville operators with general regular boundary conditions. Using these formulas, we find sufficient conditions on the potential q such that the root functions of these operators do not form a Riesz basis.

2010 Math. Subj. Class. 34L05, 34L20.

Keywords: Asymptotic formulas, regular boundary conditions, Riesz basis.

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