Matrix Chebyshev polynomials and continued fractions

DOI10.1016/S0024-3795(01)00421-9zbMath1025.42015MaRDI QIDQ5956247

Marcin J. Zygmunt

Publication date: 20 February 2002

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Blumenthal theoremmatrix Chebyshev polynomialsmatrix orthogonal polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (13)

Otto Blumenthal (1876--1944) in retrospect ⋮ Three-term recurrence relation coefficients and continued fractions related to orthogonal matrix polynomials on the finite interval [a, b] ⋮ Zeros and ratio asymptotics for matrix orthogonal polynomials ⋮ Some comments on quasi-birth-and-death processes and matrix measures ⋮ Relations between the orthogonal matrix polynomials on \([a,b\), Dyukarev-Stieltjes parameters, and Schur complements] ⋮ Relative asymptotics for orthogonal matrix polynomials ⋮ Band structure of the spectra of Hamiltonians of regular polynucleotide duplexes ⋮ A note on the maximization of matrix valued Hankel determinants with applications ⋮ \(C_{0}\)-operator orthogonal Chebyshev polynomials and their representations ⋮ Random block matrices and matrix orthogonal polynomials ⋮ Orthogonality measures for orthogonal matrix polynomials with periodic coefficients of recurrence relations ⋮ On Dyukarev's resolvent matrix for a truncated Stieltjes matrix moment problem under the view of orthogonal matrix polynomials ⋮ Weak convergence for orthogonal matrix polynomials

Cites Work

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• Ratio asymptotics for orthogonal matrix polynomials
• The early history of the moment problem
• Matrix continued fractions
• The truncated Hamburger matrix moment problems in the nondegenerate and degenerate cases, and matrix continued fractions
• Markov's theorem revisited
• Zero asymptotic behaviour for orthogonal matrix polynomials
• Orthogonal matrix polynomials: zeros and Blumenthal's theorem
• A Pincherle theorem for matrix continued fractions
• A generalization of Favard's theorem for polynomials satisfying a recurrence relation
• Markov's Theorem for Orthogonal Matrix Polynomials
• THE SCATTERING PROBLEM FOR A DISCRETE STURM-LIOUVILLE OPERATOR
• On Orthogonal Polynomials With Respect to a Positive Definite Matrix of Measures
• Noncommutative Continued Fractions

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