A new proof of Bronshtein's theorem

Adam Parusinski (1) , Armin Rainer

1 LJAD - Laboratoire Jean Alexandre Dieudonné

We give a new proof of Bronshtein's theorem: any continuous parameterization of the roots of a $C^{n-1,1}$-family of monic hyperbolic polynomials of degree $n$ is locally Lipschitz with uniform Lipschitz constants.

Domaines: Analyse classique [math.CA]

Adam Parusinski, Armin Rainer. A new proof of Bronshtein's theorem. Journal of Hyperbolic Differential Equations, 2015, 12 (4), pp.671-688. ⟨10.1142/S0219891615500198⟩. ⟨hal-00940978⟩