Nevanlinna-Pick problem and uniqueness of left inverses in convex domains, symmetrized bidisc and tetrablock

DOI10.1007/s12220-015-9611-9zbMath1350.32020arXiv1303.0482OpenAlexW1997977064MaRDI QIDQ2631015

Łukasz Kosiński, Włodzimierz Zwonek

Publication date: 28 July 2016

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

Full work available at URL: https://arxiv.org/abs/1303.0482

zbMATH Keywords

left inversetetrablocksymmetrized bidisccomplex geodesicNevanlinna-Pick problemstrongly linearly convex domain

Mathematics Subject Classification ID

Invariant metrics and pseudodistances in several complex variables (32F45) Linear operator methods in interpolation, moment and extension problems (47A57) Other notions of convexity in relation to several complex variables (32F17)

Related Items (20)

Three-point Nevanlinna–Pick problem in the polydisc ⋮ A geometric characterization of the symmetrized bidisc ⋮ A Schwarz lemma for the symmetrized polydisc via estimates on another family of domains ⋮ Nonuniqueness of Carathéodory extremal functions on the symmetrized bidisc ⋮ On the geometry of the symmetrized bidisc ⋮ Determining sets for holomorphic functions on the symmetrized bidisk ⋮ Nevanlinna-Pick interpolation problem in the ball ⋮ Geodesics, Retracts, and the Norm-Preserving Extension Property in the Symmetrized Bidisc ⋮ Norm preserving extensionsof bounded holomorphic functions ⋮ Rational tetra-inner functions and the special variety of the tetrablock ⋮ Slice rigidity property of holomorphic maps Kobayashi-isometrically preserving complex geodesics ⋮ A generalized Schwarz lemma for two domains related to \(\mu\)-synthesis ⋮ Coman conjecture for the bidisc ⋮ Interpolation by holomorphic maps from the disc to the tetrablock ⋮ Intrinsic directions, orthogonality, and distinguished geodesics in the symmetrized bidisc ⋮ Structure theorems for operators associated with two domains related to \(\mu \)-synthesis ⋮ Characterizations of the symmetrized polydisc via another family of domains ⋮ Extension Property and Universal Sets ⋮ Characterizations of some domains via Carathéodory extremals ⋮ A model theory for operators associated with a domain related to \(\mu\)-synthesis

Cites Work

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• The Lempert theorem and the tetrablock
• Hilbert function spaces and the Nevanlinna-Pick problem on the polydisc
• The magic functions and automorphisms of a domain
• Retracts in polydisk and analytic varieties with the \(H^\infty\)-extension property
• 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
• The hyperbolic geometry of the symmetrized bidisc
• Geometric properties of the tetrablock
• A Schwarz lemma for a domain related to \(\mu\)-synthesis
• Geometry of quasi-circular domains and applications to tetrablock
• The automorphism group of the tetrablock
• An example of a bounded $\mathsf C$-convex domain which is not biholomorphic to a convex domain
• Schwarz lemma for the tetrablock
• La métrique de Kobayashi et la représentation des domaines sur la boule
• THE SYMMETRIZED BIDISC AND LEMPERT'S THEOREM
• THE COMPLEX GEODESICS OF THE SYMMETRIZED BIDISC
• DESCRIPTION OF ALL COMPLEX GEODESICS IN THE SYMMETRIZED BIDISC
• Invariant distances and metrics in complex analysis

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