Maximal univalent disks of real rational functions and Hermite-Biehler polynomials

DOI10.1090/S0002-9939-2010-10778-5zbMath1223.26033arXiv1005.1596OpenAlexW4297950644MaRDI QIDQ3003575

Mikhail Tyaglov, Vladimir Petrov Kostov, Boris Zalmanovich Shapiro

Publication date: 27 May 2011

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

Full work available at URL: https://arxiv.org/abs/1005.1596

zbMATH Keywords

Hermite-Biehler theoremroot localization

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Real polynomials: analytic properties, etc. (26C05)

Related Items (3)

A generalized Hermite-Biehler theorem and non-Hermitian perturbations of Jacobi matrices ⋮ Criterion of the reality of zeros in a polynomial sequence satisfying a three-term recurrence relation ⋮ Problems around polynomials: the good, the bad and the ugly\dots

Cites Work

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• Zeros of the Wronskian of a polynomial
• Obreschkoff's theorem revisited: What convex sets are contained in the set of hyperbolic polynomials?
• The Wronski map and Grassmannians of real codimension 2 subspaces.
• Degrees of real Wronski maps
• On Critical Points of Proper Holomorphic Maps on The Unit Disk
• The Schwarzian derivative and schlicht functions

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