A New Proof of Bronshtein’s Theorem
نویسنده
چکیده
We give a new self-contained proof of Bronshtein’s theorem, that any continuous root of a Cn−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, Orrú, and Pernazza, that a C-curve of hyperbolic polynomials of degree n admits a C-system of its roots.
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