Electron. J. Diff. Eqns., Vol. 2009(2009), No. 27, pp. 1-8.

Regularized trace of the Sturm-Liouville operator with irregular boundary conditions

Alexander Makin

We consider the spectral problem for the Sturm-Liouville equation with a complex-valued potential $q(x)$ and with irregular boundary conditions on the interval $(0,\pi)$. We establish a formula for the first regularized trace of the this operator.

Submitted January 8, 2009. Published February 3, 2009.
Math Subject Classifications: 34L05, 34B24.
Key Words: Sturm-Liouville operator; eigenvalue problem; spectrum.

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Alexander Makin
Moscow State University of Instrument-Making and Informatics
Stromynka 20, Moscow, 107996, Russia
email: alexmakin@yandex.ru

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