62 citations · 389 across the 51 of their papers we have counts for
14 papers · 1 filter
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…
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…
Hölder--Zygmund classes on smooth curves
Armin Rainer
We prove that a function in several variables is in the local Zygmund class if and only if its composite with every smooth curve is of class .…
Ultradifferentiable extension theorems: a survey
Armin Rainer
We survey ultradifferentiable extension theorems, i.e., quantitative versions of Whitney's classical extension theorem, with special emphasis on the existence of continuous linear…
Ultraholomorphic sectorial extensions of Beurling type
David Nicolas Nenning, Armin Rainer, Gerhard Schindl
We prove sectorial extension theorems for ultraholomorphic function classes of Beurling type defined by weight functions with a controlled loss of regularity. The proofs are based…