On periodic boundary value problem for the Sturm-Liouville operator

Mathematics – Spectral Theory

Scientific paper

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Published in Proceedings of the International Conference "Function Spaces, Approximation Theory, Nonlinear Analysis", Moscow,

Scientific paper

We consider the Sturm-Liouville operator Lu=u''-q(x)u with periodic or
antiperiodic boundary conditions. It is shown that depending of Fourier
coefficients of the potential q(x) the system of root functions may have or may
not have the basis property.

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