A special case of de Branges' theorem on the inverse monodromy problem

DOI10.1007/BF01195820zbMath0973.46019MaRDI QIDQ5931980

Peter Yuditskii

Publication date: 5 December 2001

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

zbMATH Keywords

comb-like domainsde Branges' theoremdirect Cauchy theoreminfinite dimensional Jacobi inversioninvariant subspaces of Hardy spacesinverse monodromy problemLevin's uniqueness theoremRiemann surfaces of infinite genus

Mathematics Subject Classification ID

General spectral theory of ordinary differential operators (34L05) General theory of ordinary differential operators (47E05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Inverse problems involving ordinary differential equations (34A55) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (7)

On the \(L^1\) extremal problem for entire functions ⋮ Applications of de Branges Spaces of Vector-Valued Functions ⋮ Ahlfors problem for polynomials ⋮ Kotani-Last problem and Hardy spaces on surfaces of Widom type ⋮ On a family of Laurent polynomials generated by \(2\times 2\) matrices ⋮ On the direct Cauchy theorem in Widom domains: positive and negative examples ⋮ Schrödinger operators and de Branges spaces.

Cites Work

• Hardy classes on infinitely connected Riemann surfaces
• Critical points of Green's function, harmonic measure, and the corona problem
• Almost periodic Jacobi matrices with homogeneous spectrum, infinite dimensional Jacobi inversion, and Hardy spaces of character-automorphic functions
• \(J\)-inner matrix functions, interpolation and inverse problems for canonical systems. I: Foundations
• \(J\)-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
• The maximum principle for multiple-valued analytic functions
• On the Green's function of Fuchsian groups
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