Serikova I. Interpolation problems in the class R[a,b] and S[a,b]

In the dissertation is investigated. Necessary and sufficient solvability conditions for the matrix Nevanlinna-Pick problems with an infinite number of interpolation points in the classes R[a,b] and S[a,b] have been proved. The criterion of complete indetermination for these problems in terms of convergence of two series, where the elements are orthogonal systems of rational matrix function (MF), has been obtained. Explicit formulas expressing this MF through interpolation data has been proved. The generalized Stieltjes criterion in terms of two series convergence has been also proved. An explicit formula for generalized Stieltjes parameters has been found. The set of solutions of complete indetermination interpolation problem in the classes R[a,b] and S[a,b] in terms of linear fractional transformations has been obtained. The multiplicative structure of the resolvent matrix moment problem on a compact interval has been investigated. The explicit formulas for generalized Blaschke-Potapov factors have been obtained. Step by step process solution matrix moment problem on a compact interval has been considered.