Interpolation problems, extensions of symmetric operators and reproducing kernel spaces. II

DOI10.1007/BF01204261zbMath0787.47013MaRDI QIDQ5905416

Daniel Alpay, Piet Bruinsma, Hendrik S. V. de Snoo, Aalt Dijksma

Publication date: 26 June 1992

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

zbMATH Keywords

de Branges theory of Hilbert spaces of analytic functionsDym's method to solve interpolation problemsinterpolation problems for pairs of matrix functions of the extended Nevanlinna classKreĭn-Langer theory of extensions of symmetric operators

Mathematics Subject Classification ID

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)

Related Items (19)

The two-sided residue interpolation in the Stieltjes class of matrix functions ⋮ Classes of pairs of meromorphic matrix valued functions generated by nonnegative kernels and associated Nevanlinna-Pick problems ⋮ On tangential \(H_ 2\) interpolation with second order norm constraints ⋮ On a new positive extension problem for block Toeplitz matrices ⋮ Multiple point interpolation in Nevanlinna classes ⋮ Interpolation with symmetry and a Herglotz theorem in the bicomplex setting ⋮ A generalized Schur-Takagi interpolation problem ⋮ Boundary interpolation in the ball ⋮ A theorem on reproducing kernel Hilbert spaces of pairs ⋮ Pontryagin spaces of entire functions. I ⋮ Carathéodory Fejér interpolation in the ball with mixed derivatives ⋮ Interpolation theory in sectorial Stieltjes classes and explicit system solutions ⋮ Rigidity theorems, boundary interpolation and reproducing kernels for generalized Schur functions ⋮ Nonstationary analogs of the Herglotz representation theorem: The discrete case ⋮ Boundary interpolation for slice hyperholomorphic Schur functions ⋮ Stability and McMillan degree for rational matrix interpolants ⋮ Carathéodory - Fejér Problem for Pairs of Meromorphic Functions ⋮ Degenerate interpolation problems for Nevanlinna pairs ⋮ Carathéodory--Fejér interpolation in the ball.

Cites Work

• Hilbert spaces of analytic functions, inverse scattering and operator models. I
• Hilbert spaces of analytic functions, inverse scattering and operator models. II
• Degenerate interpolation problems for Nevanlinna pairs
• Minimal factorization of matrix and operator functions
• Self-adjoint extensions of symmetric subspaces
• Models for noncontractions
• Sous-espaces d'espaces vectoriels topologiques et noyaux associés. (Noyaux reproduisants.)
• All optimal Hankel-norm approximations of linear multivariable systems and theirL,^∞-error bounds†
• Complementation in Krein Spaces
• Some Hilbert Spaces of Analytic Functions
• Theory of Reproducing Kernels
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