\(J\)-inner matrix functions, interpolation and inverse problems for canonical systems. I: Foundations

DOI10.1007/BF01193811zbMath0902.30026OpenAlexW1964799612MaRDI QIDQ1378136

Harry Dym, Damir Z. Arov

Publication date: 4 March 1998

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

Full work available at URL: https://doi.org/10.1007/bf01193811

zbMATH Keywords

inverse problemsreproducing kernelSchur interpolation problem\(J\)-inner matrix valued functions

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) Moment problems and interpolation problems in the complex plane (30E05) Nonlinear ordinary differential operators (34L30) Entire and meromorphic functions of one complex variable, and related topics (30D99)

Related Items (20)

Criteria for the strong regularity of \(J\)-inner functions and \(\gamma\)-generating matrices. ⋮ The bitangential inverse spectral problem for canonical systems ⋮ Weyl–Titchmarsh $M$-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators ⋮ On the \(L^1\) extremal problem for entire functions ⋮ Two-Dimensional Hamiltonian Systems ⋮ B-regular J-inner Matrix-valued Functions ⋮ Scaling limits of Jacobi matrices and the Christoffel-Darboux kernel ⋮ Bitangential interpolation in generalized Schur classes ⋮ On three Klein extension problems and some generalizations ⋮ \(J\)-inner matrix functions, interpolation and inverse problems for canonical systems. II: The inverse monodromy problem ⋮ \(J\)-inner matrix functions, interpolation and inverse problems for canonical systems. III: More on the inverse monodromy problem ⋮ A special case of de Branges' theorem on the inverse monodromy problem ⋮ Scattering theory for CMV matrices: Uniqueness, Helson-Szegő and strong Szegő theorems ⋮ Matricial Nehari problems, \(J\)-inner matrix functions and the Muckenhoupt condition ⋮ The absolutely continuous spectrum of discrete canonical systems ⋮ Jacobi matrices with lacunary spectrum ⋮ Boundary-value problems for two-dimensional canonical systems ⋮ \(J\)-inner matrix functions, interpolation and inverse problems for canonical systems. IV: Direct and inverse bitangential input scattering problems ⋮ \(J\)-inner matrix functions, interpolation and inverse problems for canonical systems. V: The inverse input scattering problem for Wiener class and rational \(p\times q\) input scattering matrices ⋮ Schrödinger operators and de Branges spaces.

Cites Work

• Hilbert spaces of analytic functions, inverse scattering and operator models. I
• Hilbert spaces of analytic functions, inverse scattering and operator models. II
• The comparison theorem for Hilbert spaces of entire functions
• Left and right Blaschke-Potapov products and Arov-singular matrix-valued functions
• Regular and singular J-inner matrix-functions and the corresponding interpolation problems
• The functional model of a \(J\)-unitary node with a given \(J\)-inner characteristic matrix function
• On a new class of structured reproducing kernel spaces
• Singularities of analytic foliations and characteristic classes
• Computation of the resolvent matrix for the generalized bitangential Schur- and Carathéodory-Nevanlinna-Pick interpolation problems in the strictly completely indeterminate case
• Weighted spaces of pseudocontinuable functions and approximations by rational functions with prescribed poles
• Some Hilbert spaces of analytic functions. II, III
• Infinite Hankel matrices and generalized Caratheodory-Fejer and Riesz problems
• On operator ranges
• Some Hilbert Spaces of Entire Functions
• Some Hilbert Spaces of Entire Functions. II
• Some Hilbert Spaces of Entire Functions. IV
• On the Theory of Matrix Valued Functions Belonging to the Smirnov Class
• Some Hilbert Spaces of Entire Functions. III
• Some Hilbert Spaces of Analytic Functions
• Theory of Reproducing Kernels
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