Rigidity theorems, boundary interpolation and reproducing kernels for generalized Schur functions

DOI10.1007/BF03321732zbMath1185.30040arXiv0709.2504OpenAlexW3101925802MaRDI QIDQ1045715

Daniel Alpay, Simeon Reich, David M. Shoikhet

Publication date: 15 December 2009

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.2504

zbMATH Keywords

rigidityreproducing kernelsboundary interpolationgeneralized Schur functions

Mathematics Subject Classification ID

Boundary value problems in the complex plane (30E25) Moment problems and interpolation problems in the complex plane (30E05) Asymptotic representations in the complex plane (30E15) Kernel functions in one complex variable and applications (30C40) Blaschke products (30J10)

Related Items (5)

Rigidity and parametric embedding of semi-complete vector fields on the unit disk ⋮ Boundary interpolation and rigidity for generalized Nevanlinna functions ⋮ A Burns–Krantz-type Theorem for Pseudo-contractive Mappings ⋮ Pseudo-contractions, rigidity, fixed points and related questions ⋮ Positive matrices in the Hardy space with prescribed boundary representations via the Kaczmarz algorithm

Cites Work

• Interpolation of rational matrix functions
• Schur functions, operator colligations, and reproducing kernel Pontryagin spaces
• Nevanlinna-Pick interpolation with boundary data
• Boundary interpolation and rigidity for generalized Nevanlinna functions
• Rigidity of Holomorphic Mappings and a New Schwarz Lemma at the Boundary
• A uniqueness result on boundary interpolation
• Generalized Interpolation in H ∞
• Interpolation problems, extensions of symmetric operators and reproducing kernel spaces. II
• Interpolation problems, extensions of symmetric operators and reproducing kernel spaces. II
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