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

Summary:

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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