Orthogonal polynomials and analytic functions associated to positive definite matrices

DOI10.1016/j.jmaa.2005.09.093zbMath1121.30017OpenAlexW2084598666MaRDI QIDQ819025

Christian Berg, Antonio J. Duran

Publication date: 22 March 2006

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2005.09.093

zbMATH Keywords

moment problemorthogonal polynomialspositive definite matricesorthogonal matrix polynomialsHankel matricesindex of indeterminacy

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Linear operator methods in interpolation, moment and extension problems (47A57) Moment problems and interpolation problems in the complex plane (30E05)

Related Items (6)

Deficiency indices of block Jacobi matrices and Miura transformation ⋮ Small eigenvalues of large Hermitian moment matrices ⋮ On the completely indeterminate case for block Jacobi matrices ⋮ Smallest and largest generalized eigenvalues of large moment matrices and some applications ⋮ The smallest eigenvalue of Hankel matrices ⋮ On the inversion of infinite moment matrices

Cites Work

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• Rotation invariant moment problems
• Orthogonal matrix polynomials and higher-order recurrence relations
• When does a discrete differential perturbation of a sequence of orthonormal polynomials belong to \(\ell^ 2\)?
• Matrix Analysis
• Measures with finite index of determinacy or a mathematical model for Dr. Jekyll and Mr. Hyde
• The Nevanlinna parametrization for a matrix moment problem
• Small eigenvalues of large Hankel matrices: The indeterminate case
• On Orthogonal Polynomials With Respect to a Positive Definite Matrix of Measures
• The Index of Determinacy for Measures and the ℓ 2 -Norm of Orthonormal Polynomials

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