7 papers
Eigenvalue stability of Hermitian and normal matrices
Adam ParusiÅski, 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…
PÅoski Approximation Theorem
Adam ParusiÅski, 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…
Continuity of the solution map for hyperbolic polynomials
Adam ParusiÅski, 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…
Definable Lipschitz selections for affine-set valued maps
Adam ParusiÅski, Armin Rainer
Whitney's extension problem, i.e., how one can tell whether a function , , is the restriction of a -function on , wa…
Perturbation theory of polynomials and linear operators
Adam ParusiÅski, 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…
On the continuity of the solution map for polynomials
Adam ParusiÅski, 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…