A note on polydegree \((n, 1)\) rational inner functions, slice matrices, and singularities

DOI10.1007/s00013-022-01812-3OpenAlexW4310917401MaRDI QIDQ2699757

Alan A. Sola

Publication date: 19 April 2023

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.08961

zbMATH Keywords

rational inner functionderivative integrabilityslice matrix

Mathematics Subject Classification ID

Boundary behavior of holomorphic functions of several complex variables (32A40) Blaschke products (30J10)

Cites Work

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• Stable symmetric polynomials and the Schur-Agler class
• Rational inner functions in the Schur-Agler class of the polydisk
• A Carathéodory theorem for the bidisk via Hilbert space methods
• Schwarz-Pick inequalities for the Schur-Agler class on the polydisk and unit ball
• Scattering systems with several evolutions and multidimensional input/state/output systems
• Schur-Agler class rational inner functions on the tridisk
• Integrability and regularity of rational functions:
• Derivatives of rational inner functions: geometry of singularities and integrability at the boundary
• Finite Blaschke Products and Their Connections
• Level curve portraits of rational inner functions
• Dynamics of low-degree rational inner skew-products on $\mathbb{T}^2$
• Singularities of rational inner functions in higher dimensions
• An Inductive Julia-Carathéodory Theorem for Pick Functions in Two Variables
• A wedge‐of‐the‐edge theorem: analytic continuation of multivariable Pick functions in and around the boundary
• Rational inner functions and their Dirichlet type norms

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