4 papers
Effective quasianalytic Remez inequalities on tame sets
Armin Rainer
We establish a Remez inequality for functions in quasianalytic Denjoy-Carleman classes on a large family of fat compact sets with tame geom…
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…
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…