On the regularity of the roots of a polynomial depending on one real parameter
type: Item
instance of: scholarly article
title: On the regularity of the roots of a polynomial depending on one real parameter
zbMATH Open document ID: 1379.26005
DOI: 10.4171/RLM/784
author: Ferruccio Colombini
author: Nicola Orrù
author: Ludovico Pernazza
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2018-01-04T00:00:00Z
review text: Summary: We investigate the regularity of functions \(\tau\) of one variable such that \(P(t,\tau(t))=0\), where \(P(t,x)\) is a given polynomial of degree \(m\) in \(x\) whose coefficients are functions of class \(C^{m^2!}\) 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.
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 26A27
zbMATH DE Number: 6821668
zbMATH Keywords: square roots
zbMATH Keywords: bounded variation
zbMATH Keywords: absolute continuity
MaRDI profile type: Publication
Recommended article: Regularity of roots of polynomials
Recommended article: On the regularity of the roots of hyperbolic polynomials
Recommended article: On polynomials with only real roots
Recommended article: On the real roots of \(\sigma\)-polynomials
Recommended article: Q3356852
Recommended article: On perturbations of roots of polynomials
Recommended article: On the bounds for the roots of a polynomial
Recommended article: On the existence of complex roots of real polynomials
Recommended article: Q3755545
Recommended article: On the number of real roots of a solvable polynomial
description: scientific article; zbMATH DE number 6821668