Abstract:By using Schur transformed sequences and Dyukarev-Stieltjes parameters we obtain a new representation of the resolvent matrix corresponding to the truncated matricial Stieltjes moment problem. Explicit relations between orthogonal matrix polynomials and matrix polynomials of the second kind constructed from consecutive Schur transformed sequences are obtained. Additionally, a non-negative Hermitian measure for which the matrix polynomials of the second kind are the orthogonal matrix polynomials is found.
“…Kovalishina [37], [38], H. Dym [22], B. Simon [44], Damanik/Pushnitski/-Simon [15] and the references therein. See also [17], [18], [19], [20], [21], [34], [16], [41], [45], [31], [12], [13], [11], [6] and [7].…”
A new multiplicative decomposition of the resolvent matrix of the truncated Hausdorff matrix moment (THMM) problem in the case of an odd and even number of moments via new Dyukarev-Stieltjes matrix (DSM) parameters is attained. Additionally, we derive Blaschke-Potapov factors of auxiliary resolvent matrices; each factor is decomposed with the help of the DSM parameters.
“…Kovalishina [37], [38], H. Dym [22], B. Simon [44], Damanik/Pushnitski/-Simon [15] and the references therein. See also [17], [18], [19], [20], [21], [34], [16], [41], [45], [31], [12], [13], [11], [6] and [7].…”
A new multiplicative decomposition of the resolvent matrix of the truncated Hausdorff matrix moment (THMM) problem in the case of an odd and even number of moments via new Dyukarev-Stieltjes matrix (DSM) parameters is attained. Additionally, we derive Blaschke-Potapov factors of auxiliary resolvent matrices; each factor is decomposed with the help of the DSM parameters.
Relations between the orthogonal matrix polynomials on [a, b] Abstract: We obtain explicit interrelations between new Dyukarev-Stieltjes matrix parameters and orthogonal matrix polynomials on a nite interval [a, b], as well as the Schur complements of the block Hankel matrices constructed through the moments of the truncated Hausdor matrix moment (THMM) problem in the nondegenerate case. Extremal solutions of the THMM problem are described with the help of matrix continued fractions.
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