Retracts in polydisk and analytic varieties with the \(H^\infty\)-extension property

DOI10.1007/s12220-007-9005-8zbMath1156.32003OpenAlexW2102023196MaRDI QIDQ941845

Kai Wang, Kunyu Guo, Hansong Huang

Publication date: 2 September 2008

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-007-9005-8

zbMATH Keywords

iterationretract\(H^\infty\)-convex property\(H^\infty\)-extension propertyanalytic variety

Mathematics Subject Classification ID

Continuation of analytic objects in several complex variables (32D15) Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Linear operator methods in interpolation, moment and extension problems (47A57) Hilbert spaces of continuous, differentiable or analytic functions (46E20)

Related Items

Nevanlinna-Pick problem and uniqueness of left inverses in convex domains, symmetrized bidisc and tetrablock ⋮ Three-point Nevanlinna–Pick problem in the polydisc ⋮ A uniqueness theorem for bounded analytic functions on the polydisc ⋮ Complete norm-preserving extensions of holomorphic functions ⋮ Pairs of inner projections and two applications ⋮ Polynomial extension property in the classical Cartan domain \(\mathcal{R}_{II}\) ⋮ Geodesics, Retracts, and the Norm-Preserving Extension Property in the Symmetrized Bidisc ⋮ Hilbert function spaces and the Nevanlinna-Pick problem on the polydisc. II. ⋮ Norm preserving extensionsof bounded holomorphic functions ⋮ On polynomial extension property in $n$-disc ⋮ Hilbert function spaces and the Nevanlinna-Pick problem on the polydisc ⋮ Extensions of bounded holomorphic functions on the tridisk ⋮ Extension Property and Universal Sets

Cites Work

• Cusp algebras
• Holomorphic retracts in complex n-space
• Unitary colligations, reproducing kernel Hilbert spaces, and Nevanlinna-Pick interpolation in several variables
• Norm preserving extensions of holomorphic functions from subvarieties of the bidisk
• The three point pick problem on the bidisk
• Distinguished varieties
• Toral algebraic sets and function theory on polydisks
• Extending bounded holomorphic functions from certain subvarieties of a polydisc
• On convergence to the Denjoy-Wolff point
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