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We investigate the regularity of functions of one variable such that , where is a given polynomial of degree in whose coefficients are functions of class of one real parameter. We show that if a root is chosen with a continuous dependence on the parameter, this function is indeed absolutely continuous. From this and a theorem of Kato one deduces that such polynomials have complete systems of roots that are absolutely continuous functions.
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Ferruccio Colombini, Nicola Orrù, Ludovico Pernazza, On the regularity of the roots of a polynomial depending on one real parameter. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28 (2017), no. 4, pp. 747–775