On 28.09.2016, at 11.20 the seminar of the department of «Differential Equations» will be held. At the seminar leading researcher of Institute of Mathematics and Mechanics Telman Benser oglu Gasymov will give a talk on « SOME PROBLEMS OF SPECTRAL THEORY OF DISCONTINUOUS DIFFERENTIAL OPERATORS ».

The report is devoted to the spectral problems for ordinary differential and quasi-differential operators with discontinuous multipoint and integral boundary conditions. The concepts of regularity and strengthened regularity of the boundary conditions are introduced and the theorems on basicity of eigen and associated functions of a regular boundary-value problems are proved.

Abstract theorems are proved on the basicity of some systems in X ⊕ C ^m and X = X₁ ⊕ …. ⊕ X_m , type Banach spaces which have applications in the spectral theory of discontinuous differential operators, as well as in spectral problems containing the spectral parameter in the boundary conditions.