1 citations · 1 across the 7 of their papers we have counts for
8 papers
Natural reparameterization and continuity of the solution map for polynomials
Adam Parusiński, Armin Rainer
The optimal Sobolev regularity of the roots of a smooth curve of monic complex polynomials is , for , where is the degree. This result is stab…
Eigenvalue stability of Hermitian and normal matrices
Adam Parusiński, Armin Rainer
The ordered eigenvalues define a Lipschitz map on the real vector space of Hermitian matrices. We prove that this map acts continuously, but not uniformly continuously…
Płoski Approximation Theorem
Adam Parusiński, Guillaume Rond
The aim of this paper is to review how some approximation results in commutative algebra are being used to construct equisingular deformations of singularities. The first example o…
On the continuity of the solution map for polynomials
Adam Parusiński, Armin Rainer
In previous work, we proved that the continuous roots of a monic polynomial of degree whose coefficients depend in a way on real parameters belong to the Sobolev sp…
Continuity of the solution map for hyperbolic polynomials
Adam Parusiński, Armin Rainer
Hyperbolic polynomials are monic real-rooted polynomials. By Bronshtein's theorem, the increasingly ordered roots of a hyperbolic polynomial of degree with coeffici…
Perturbation theory of polynomials and linear operators
Adam Parusiński, Armin Rainer
This survey revolves around the question how the roots of a monic polynomial (resp. the spectral decomposition of a linear operator), whose coefficients depend in a smooth way on p…
Uniform extension of definable -Whitney jets
Adam Parusiński, Armin Rainer
We show that definable Whitney jets of class , where is a nonnegative integer and is a modulus of continuity, are the restrictions of definable -functions…
Definable Lipschitz selections for affine-set valued maps
Adam Parusiński, Armin Rainer
Whitney's extension problem, i.e., how one can tell whether a function , , is the restriction of a -function on , wa…