Holomorphic functions on the symmetrized bidisk - realization, interpolation and extension

DOI10.1016/j.jfa.2017.09.013zbMath1384.32003arXiv1511.08962OpenAlexW2270742683MaRDI QIDQ1677457

Tirthankar Bhattacharyya, Haripada Sau

Publication date: 21 November 2017

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.08962

zbMATH Keywords

Nevanlinna-Pick interpolationextension of holomorphic functionssymmetrized bidisk

Mathematics Subject Classification ID

Continuation of analytic objects in several complex variables (32D15) Moment problems and interpolation problems in the complex plane (30E05) (H^p)-spaces, Nevanlinna spaces of functions in several complex variables (32A35) Other generalizations of function theory of one complex variable (32A30) Holomorphic functions of several complex variables (32A10)

Related Items (12)

A Schwarz lemma for the symmetrized polydisc via estimates on another family of domains ⋮ Realization of functions on the symmetrized bidisc ⋮ Norm preserving extensions of holomorphic functions defined on varieties in \(\mathbb{C}^n\) ⋮ Determining sets for holomorphic functions on the symmetrized bidisk ⋮ Interpolating sequences for the Banach algebras generated by a class of test functions ⋮ The symmetrization map and \(\Gamma\)-contractions ⋮ Polynomial extension property in the classical Cartan domain \(\mathcal{R}_{II}\) ⋮ Geodesics, Retracts, and the Norm-Preserving Extension Property in the Symmetrized Bidisc ⋮ On the Nevanlinna problem: characterization of all Schur–Agler class solutions affiliated with a given kernel ⋮ Algebraic properties of Toeplitz operators on the symmetrized polydisk ⋮ Characterizations of the symmetrized polydisc via another family of domains ⋮ Extension Property and Universal Sets

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• Multivariable Generalizations of the Schur Class: Positive Kernel Characterization and Transfer Function Realization
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