On the continuity of the solution map for polynomials

2024/10/02 by Parusiński, Adam, Rainer, Armin
#Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2410.01326

Abstract

In previous work, we proved that the continuous roots of a monic polynomial of degree d whose coefficients depend in a C^d-1,1 way on real parameters belong to the Sobolev space W^1,q for all 1≤ q

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