Abstract
We prove that a hyperbolic monic polynomial whose coefficients are functions of class C r of a parameter t admits roots of class C 1 in t, if r is the maximal multiplicity of the roots as t varies. Moreover, if the coefficients are functions of t of class C 2r, then the roots may be chosen two times differentiable at every point in t. This improves, among others, previous results of Bronšteĭn, Mandai, Wakabayashi and Kriegl, Losik and Michor.
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Colombini, F., Orrù, N. & Pernazza, L. On the regularity of the roots of hyperbolic polynomials. Isr. J. Math. 191, 923–944 (2012). https://doi.org/10.1007/s11856-012-0015-2
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DOI: https://doi.org/10.1007/s11856-012-0015-2