On Hankel nonnegative definite sequences, the canonical Hankel parametrization, and orthogonal matrix polynomials

DOI10.1007/s11785-010-0054-9zbMath1298.05016OpenAlexW2051261265MaRDI QIDQ644427

Conrad Mädler, Bernd Kirstein, Bernd Fritzsche

Publication date: 4 November 2011

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-010-0054-9

zbMATH Keywords

orthogonal matrix polynomialsHankel nonnegative definite sequencesnonnegative Hermitian block Hankel matricesnonnegative Hermitian measurescanonical Hankel parametrizationCatalan parametrizationgeneralized Lucas numbersHankel nonnegative definite extendable sequencessequences of moments of classical probability distributionstruncated matricial Hamburger moment problem

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Permutations, words, matrices (05A05) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Linear operator methods in interpolation, moment and extension problems (47A57) Moment problems (44A60) Orthogonal matrices (15B10)

Related Items (18)

Parametrization of the Solution Set of a Matricial Truncated Hamburger Moment Problem by a Schur Type Algorithm ⋮ Three-term recurrence relation coefficients and continued fractions related to orthogonal matrix polynomials on the finite interval [a, b] ⋮ The Weyl matrix balls corresponding to the matricial truncated Hamburger moment problem ⋮ Schur analysis of matricial Hausdorff moment sequences ⋮ Dyukarev-Stieltjes parameters of the truncated Hausdorff matrix moment problem ⋮ Relations between the orthogonal matrix polynomials on \([a,b\), Dyukarev-Stieltjes parameters, and Schur complements] ⋮ Transformations of matricial \({\alpha}\)-Stieltjes non-negative definite sequences ⋮ A Potapov-Type Approach to a Truncated Matricial Stieltjes-Type Power Moment Problem ⋮ On Hankel positive definite perturbations of Hankel positive definite sequences and interrelations to orthogonal matrix polynomials ⋮ On the Structure of Hausdorff Moment Sequences of Complex Matrices ⋮ From the Potapov to the Krein-Nudel'man representation of the resolvent matrix of the truncated Hausdorff matrix moment problem ⋮ A Closer Look at the Solution Set of the Truncated Matricial Moment Problem "Equation missing" ⋮ On a simultaneous approach to the even and odd truncated matricial Stieltjes moment problem I: an \(\alpha\)-Schur-Stieltjes-type algorithm for sequences of complex matrices ⋮ New ``Verblunsky-type coefficients of block Toeplitz and Hankel matrices and of corresponding Dirac and canonical systems ⋮ The matrix Toda equations for coefficients of a matrix three-term recurrence relation ⋮ Matricial canonical moments and parametrization of matricial Hausdorff moment sequences ⋮ Weyl sets in a truncated matricial Stieltjes moment problem ⋮ On Dyukarev's resolvent matrix for a truncated Stieltjes matrix moment problem under the view of orthogonal matrix polynomials

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