On a new class of reproducing kernel spaces and a new generalization of the Iohvidov laws

DOI10.1016/0024-3795(93)90339-PzbMath0807.46026WikidataQ126572844 ScholiaQ126572844MaRDI QIDQ1208285

Daniel Alpay, Harry Dym

Publication date: 16 May 1993

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

zbMATH Keywords

factorizationsSchur complementsGram matrixmatrix valued functioninvertible Hermitian matrixfinite dimensional reproducing kernel spaces of \(m\times 1\) vector valued analytic functions

Mathematics Subject Classification ID

Factorization of matrices (15A23) Theory of matrix inversion and generalized inverses (15A09) 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) Matrix pencils (15A22) Kernel functions in one complex variable and applications (30C40)

Related Items (13)

On a general moment problem and certain matrix equations ⋮ Schur Analysis in an Indefinite Setting ⋮ Classes of pairs of meromorphic matrix valued functions generated by nonnegative kernels and associated Nevanlinna-Pick problems ⋮ More on maximum entropy interpolants and maximum determinant completions of associated Pick matrices ⋮ Discrete analytic functions, structured matrices and a new family of moment problems ⋮ On a new class of realization formulas and their application ⋮ The Schur algorithm for generalized Schur functions. III: \(J\)-unitary matrix polynomials on the circle. ⋮ A Schur transformation for functions in a general class of domains ⋮ Beurling-Lax type theorems in the complex and quaternionic setting ⋮ Boundary interpolation in the ball ⋮ On degenerate interpolation, entropy and extremal problems for matrix Schur functions ⋮ Realizations for Schur upper triangular operators centered at an arbitrary point ⋮ On fischer-frobenius transformations and the structure of rectangular block hankel matrices

Cites Work

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• Algebraic methods for Toeplitz-like matrices and operators
• On hermitian block Hankel matrices, matrix polynomials, the Hamburger moment problem, interpolation and maximum entropy
• Structured invariant spaces of vector valued rational functions, Hermitian matrices, and a generalization of the Iohvidov laws
• Structured invariant spaces of vector valued functions, sesquilinear forms, and a generalization of the Iohvidov laws
• On the inverses of Toeplitz-plus-Hankel matrices
• Displacement ranks of matrices and linear equations
• Asymptotically fast solution of Toeplitz and related systems of linear equations
• Theory of Reproducing Kernels

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