Methods of Functional Analysis and Topology, 2009, № 1 http://dspace.nbuv.gov.ua:80/handle/123456789/5694 2026-04-29T09:34:21Z 2026-04-29T09:34:21Z Direct Spectral Problem for the Generalized Jacobi Hermitian Matrices Ivasiuk, I.Ya http://dspace.nbuv.gov.ua:80/handle/123456789/5704 2010-02-03T10:01:06Z 2009-01-01T00:00:00Z Direct Spectral Problem for the Generalized Jacobi Hermitian Matrices Ivasiuk, I.Ya In this article we will introduce and investigate some generalized Jacobi matrices. These matrices have three-diagonal block structure and they are Hermitian. We will give necessary and sufficient conditions for selfadjointness of the operator which is generated by the matrix of such a type, and consider its generalized eigenvector expansion. 2009-01-01T00:00:00Z Origination of the Singular Continuous Spectrum in the Conflict Dynamical Systems Karataieva, T. Koshmanenko, V. http://dspace.nbuv.gov.ua:80/handle/123456789/5703 2010-02-03T10:01:09Z 2009-01-01T00:00:00Z Origination of the Singular Continuous Spectrum in the Conflict Dynamical Systems Karataieva, T.; Koshmanenko, V. We study the spectral properties of the limiting measures in the conflict dynamical systems modeling the alternative interaction between opponents. It has been established that typical trajectories of such systems converge to the invariant mutually singular measures. We show that "almost always" the limiting measures are purely singular continuous. Besides we find the conditions under which the limiting measures belong to one of the spectral type: pure singular continuous, pure point, or pure absolutely continuous. 2009-01-01T00:00:00Z Spectral Gaps of the One-Dimensional Schrödinger Operators with Singular Periodic Potentials Mikhailets, V. Molyboga, V. http://dspace.nbuv.gov.ua:80/handle/123456789/5702 2010-02-03T10:01:03Z 2009-01-01T00:00:00Z Spectral Gaps of the One-Dimensional Schrödinger Operators with Singular Periodic Potentials Mikhailets, V.; Molyboga, V. 2009-01-01T00:00:00Z Inverse Eigenvalue Problems for Nonlocal Sturm-Liouville Operators Nizhnik, L.P. http://dspace.nbuv.gov.ua:80/handle/123456789/5701 2010-02-03T10:01:06Z 2009-01-01T00:00:00Z Inverse Eigenvalue Problems for Nonlocal Sturm-Liouville Operators Nizhnik, L.P. We solve the inverse spectral problem for a class of Sturm - Liouville operators with singular nonlocal potentials and nonlocal boundary conditions. 2009-01-01T00:00:00Z