Weekly seminar april  01, 2015, 10.00 a.m.  featured a report  by prof. Ziyatkhan Seyfaddin oglu Aliyev, leading researcher of the Department of  Non-Harmonic Analysis, entitled “Some spectral properties of the Sturm-Liouville operator with spectral parameter in the boundary conditions ”.

We consider the Sturm-Liouville problem with spectral parameter in both boundary conditions. This problem is reduced to the spectral problem for a self-adjoint operator acting in a Hilbert space or in a Pontryagin space. Using the method of spectral theory of operators in Hilbert spaces and spaces with an indefinite metric and the analyst-processing techniques is given general charac-teristics of the location of eigenvalues in the complex plane (on the real axis), to study the structure of the root subspaces and oscillation properties of eigenfunctions of this problem. Also, we give sufficient conditions for a basis subsystems of the root functions in spaces.

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