On hermitian block Hankel matrices, matrix polynomials, the Hamburger moment problem, interpolation and maximum entropy

DOI10.1007/BF01196878zbMath0704.47009OpenAlexW2033532497MaRDI QIDQ916985

Harry Dym

Publication date: 1989

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01196878

zbMATH Keywords

interpolation problemDe Branges spacesde Branges pairesmaximum entropy solutionsnumber of roots of certain matrix polynomialsorthogonal matrix polynomials associated with a block Hankel matrixpositive defined block Hankel matrixreproducing kernel space methodstruncated matrix Hamburger moment problem

Mathematics Subject Classification ID

Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Linear operator methods in interpolation, moment and extension problems (47A57) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hilbert spaces of analytic functions, inverse scattering and operator models. I
• Hilbert spaces of analytic functions, inverse scattering and operator models. II
• Problem of search of the minimum of entropy in indeterminate extension problems
• Scattering theory and matrix orthogonal polynomials on the real line
• ANALYTIC THEORY OF A CLASS OF INTERPOLATION PROBLEMS
• Continued Fractions and Strong Hamburger Moment Problems
• Some Hilbert Spaces of Analytic Functions

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