http://dspace.nbuv.gov.ua:80/handle/123456789/106527 2026-04-19T08:13:11Z 2026-04-19T08:13:11Z Zubkova, E.I. Rofe-Beketov, F.S. http://dspace.nbuv.gov.ua:80/handle/123456789/106545 2016-10-01T00:01:57Z 2009-01-01T00:00:00Z

Necessary and Sufficient Conditions in Inverse Scattering Problem on the Axis for the Triangular 2 x 2 Matrix Potential Zubkova, E.I.; Rofe-Beketov, F.S. The characteristic properties of the scattering data for the Schr¨odinger operator on the axis with a triangular 2 × 2 matrix potential are obtained. A difference between the necessary and sufficient conditions for solvability of ISPunder consideration, contained in the previous works of the authors, is eliminated.

2009-01-01T00:00:00Z Zolotarev, V.A. http://dspace.nbuv.gov.ua:80/handle/123456789/106544 2016-10-01T00:01:56Z 2009-01-01T00:00:00Z

On Commutative Systems of Nonselfadjoint Unbounded Linear Operators Zolotarev, V.A. For a commutative system of nonselfadjoint unbounded operators A₁, A₂ the concept of colligation and associated open system is given. For these open systems, the consistency conditions are established and the conservation laws are obtained.

2009-01-01T00:00:00Z Poplavskyi, M. http://dspace.nbuv.gov.ua:80/handle/123456789/106543 2016-10-01T00:01:55Z 2009-01-01T00:00:00Z

Bulk Universality for Unitary Matrix Models Poplavskyi, M. A proof of universality in the bulk of spectrum of unitary matrix models, assuming that the potential is globally C² and locally C³ function (see Theorem 1.2), is given. The proof is based on the determinant formulas for correlation functions in terms of polynomials orthogonal on the unit circle. The sin-kernel is obtained as a unique solution of a certain nonlinear integrodifferential equation without using asymptotics of orthogonal polynomials.

2009-01-01T00:00:00Z Bershtein, O. Sinel’shchikov, S. http://dspace.nbuv.gov.ua:80/handle/123456789/106542 2016-10-01T00:01:42Z 2009-01-01T00:00:00Z

A q-Analog of the Hua Equations Bershtein, O.; Sinel’shchikov, S. A necessary condition is established for a function to be in the image of a quantum Poisson integral operator associated to the Shilov boundary of the quantum matrix ball. A quantum analogue of the Hua equations is introduced.

2009-01-01T00:00:00Z