Optimal Sobolev regularity of roots of polynomials

DOI10.24033/asens.2376zbMath1435.30019arXiv1506.01512OpenAlexW2338206558WikidataQ128554156 ScholiaQ128554156MaRDI QIDQ5378079

Armin Rainer, Adam Parusiński

Publication date: 11 June 2019

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.01512

zbMATH Keywords

absolute continuity of rootsoptimal regularity of the roots among Sobolev spaces \(W^{1,p}\)perturbation of complex polynomials

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Real polynomials: location of zeros (26C10) Inequalities involving derivatives and differential and integral operators (26D10) Polynomials and rational functions of one complex variable (30C10) Absolutely continuous real functions in one variable (26A46)

Related Items (4)

A regularity class for the roots of nonnegative functions ⋮ Quantitative tame properties of differentiable functions with controlled derivatives ⋮ Sobolev lifting over invariants ⋮ Selections of bounded variation for roots of smooth polynomials

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