An Inductive Julia-Carathéodory Theorem for Pick Functions in Two Variables

DOI10.1017/S0013091517000396zbMath1421.32015arXiv1605.08707OpenAlexW2964201047WikidataQ122154781 ScholiaQ122154781MaRDI QIDQ5228169

James Eldred Pascoe

Publication date: 9 August 2019

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.08707

zbMATH Keywords

moment problemsbidiskPick functions

Mathematics Subject Classification ID

Boundary behavior of holomorphic functions of several complex variables (32A40) Holomorphically convex complex spaces, reduction theory (32E05)

Related Items (6)

Singularities of rational inner functions in higher dimensions ⋮ A note on polydegree \((n, 1)\) rational inner functions, slice matrices, and singularities ⋮ Cauchy transforms arising from homomorphic conditional expectations parametrize noncommutative Pick functions ⋮ A controlled tangential Julia-Carathéodory theory via averaged Julia quotients ⋮ Level curve portraits of rational inner functions ⋮ The non-tangential boundary behavior of the matrix-valued rational inner functions on bounded symmetric domain

Cites Work

• Nevanlinna representations in several variables
• A Carathéodory theorem for the bidisk via Hilbert space methods
• Boundary behavior of analytic functions of two variables via generalized models
• The Julia-Wolff-Carathéodory theorem in polydisks
• A higher order analogue of the Carathéodory--Julia theorem
• Unitary dilations for commuting contractions
• Julia's Lemma and Wolff's Theorem For J ∗ -Algebras
• Hankel vector moment sequences and the non-tangential regularity at infinity of two variable Pick functions
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