62 citations · 389 across the 51 of their papers we have counts for
57 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…
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…
Quantitative tame properties of differentiable functions with controlled derivatives
Armin Rainer
We show that differentiable functions, defined on a convex body , whose derivatives do not exceed a suitable given sequence of positive real numbers share…
The Borel map in the mixed Beurling setting
David Nicolas Nenning, Armin Rainer, Gerhard Schindl
The Borel map takes a smooth function to its infinite jet of derivatives (at zero). We study the restriction of this map to ultradifferentiable classes of Beurling type in a very g…