Choosing roots of polynomials smoothly

1998/01/07 by Dmitri Alekseevsky, Andreas Kriegl, Mark Losik +1
Mathematics · #math.CA #math.FA #math.SP #msc:26C10 #msc:47A55

paper · pdf

published as Israel J. Math 105 (1998), p. 203-233. · to appear Israel J. Math

arxiv created 1998/01/07 · arxiv updated 2009/11/30

Abstract

We clarify the question whether for a smooth curve of polynomials one can choose the roots smoothly and related questions. Applications to perturbation theory of operators are given.

Related

• Choosing roots of polynomials smoothly, II
• Perturbation theory of polynomials and linear operators
• Smooth multiparameter perturbation of polynomials and operators
• Yet another proof that the roots of a polynomial depend continuously on the coefficients
• Lower Bounds for the Number of Smooth Values of a Polynomial