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SOME SPECTRAL PROPERTIES OF STURM-LIOUVILLE PROBLEM WITH TRANSMISSION CONDITIONS

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We investigate the boundary-value problem generated by the Sturm-Liouville equation with discontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditions at the point of discontinuity. With a different approach we introduce an adequate Hilbert space formulation, investigate some properties of eigenvalues, Greenיs function and resolvent operator, and find simple conditions on the coefficients which guarantee the self-adjointness of the considered problem.

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