http://dspace.nbuv.gov.ua:80/handle/123456789/5692 2026-04-29T08:11:27Z 2026-04-29T08:11:27Z Berezansky, Yu. http://dspace.nbuv.gov.ua:80/handle/123456789/5711 2010-02-03T10:01:15Z 2009-01-01T00:00:00Z

The Integration of Double-Infinite Toda Lattice by Means of Inverse Spectral Problem and Related Quetions Berezansky, Yu. The solution of the Cauchy problem for differential-difference double-infinite Toda lattice by means of inverse spectral problem for semi-infinite block Jacobi matrix is given. Namely, we construct a simple linear system of three differential equations of first order whose solution gives the spectral matrix measure of the aforementioned Jacobi matrix. The solution of the Cauchy problem for the Toda lattice is given by the procedure of orthogonalization w.r.t. this spectral measure, i.e. by the solution of the inverse spectral problem for this Jacobi matrix.

2009-01-01T00:00:00Z Khrabustovskyi, V. http://dspace.nbuv.gov.ua:80/handle/123456789/5710 2010-02-03T10:01:13Z 2009-01-01T00:00:00Z

Expansion in Eigenfunctions of Relations Generated by Pair of Operator Differential Expressions Khrabustovskyi, V. For relations generated by a pair of operator symmetric differential expressions, a class of generalized resolvents is found. These resolvents are integro-differential operators. The expansion in eigenfunctions of these relations is obtained.

2009-01-01T00:00:00Z Murach, A.A. http://dspace.nbuv.gov.ua:80/handle/123456789/5709 2010-02-03T10:01:12Z 2009-01-01T00:00:00Z

Extension of Some Lions-Magenes Theorems Murach, A.A. A general form of the Lions - Magenes theorems on solvability of an elliptic boundary-value problem in the spaces of nonregular distributions is proved. We find a general condition on the space of right-hand sides of the elliptic equation under which the operator of the problem is bounded and has a finite index on the corresponding couple of Hilbert spaces. Extensive classes of the spaces satisfying this condition are constructed. They contain the spaces used by Lions and Magenes and many others spaces.

2009-01-01T00:00:00Z Omel'chenko, P.V. http://dspace.nbuv.gov.ua:80/handle/123456789/5708 2010-02-03T10:01:16Z 2009-01-01T00:00:00Z

About *-Representations of Polynomial Semilinear Relations Omel'chenko, P.V. In the present paper we study *-representations of semilinear relations with polynomial characteristic functions. For any finite simple non-oriented graph Г we construct a polynomial characteristic function such that Г is its graph. Full description of graphs which satisfy polynomial (degree one and two) semilinear relations is obtained. We introduce the G-orthoscalarity condition and prove that any semilinear relation with quadratic characteristic function and condition of G-orthoscalarity is *-tame. This class of relations contains, in particular, *-representations of Uq(so(3)).

2009-01-01T00:00:00Z