A new proof of Bronshtein’s theorem

DOI10.1142/S0219891615500198zbMath1339.26032arXiv1309.2150OpenAlexW1749124642MaRDI QIDQ2804484

Armin Rainer, Adam Parusiński

Publication date: 29 April 2016

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.2150

zbMATH Keywords

Bronshtein's theoremLipschitz and \(C^1\) roots of hyperbolic polynomials

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: location of zeros (26C10) Real polynomials: analytic properties, etc. (26C05)

Related Items (6)

Lifting differentiable curves from orbit spaces ⋮ A regularity class for the roots of nonnegative functions ⋮ Minimizing memory effects of a system ⋮ Sobolev lifting over invariants ⋮ Selections of bounded variation for roots of smooth polynomials ⋮ Roots of Gårding hyperbolic polynomials

Cites Work

• Remarks on hyperbolic polynomials
• Nonnegative functions as squares or sums of squares
• Störungstheorie der Spektralzerlegung. I. Analytische Störung der isolierten Punkteigenwerte eines beschränkten Operators
• On square roots of class Cm of nonnegative functions of one variable
• On the differentiability class of the admissible square roots of regular nonnegative functions
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