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arXiv · 1309.2150

A new proof of Bronshtein's theorem

Adam Parusinski·Armin Rainer
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Abstract

We give a new self-contained proof of Bronshtein's theorem, that any continuous root of a $C^{n-1,1}$-family of monic hyperbolic polynomials of degree $n$ is locally Lipschitz, and obtain explicit bounds for the Lipschitz constant of the root in terms of the coefficients. As a by-product we reprove the recent result of Colombini, Orr\'u, and Pernazza, that a $C^n$-curve of hyperbolic polynomials of degree $n$ admits a $C^1$-system of its roots.

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Adam Parusinski, Armin Rainer. 2013-09-09. A new proof of Bronshtein's theorem. https://doi.org/10.1142/s0219891615500198

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