62 citations · 389 across the 51 of their papers we have counts for
27 papers · 1 filter
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…
Arc-smooth functions and cuspidality of sets
Armin Rainer
A function is arc-smooth if the composite with every smooth curve in its domain of definition is smooth. On open sets in smooth manifolds the arc-smooth function…
Nonlinear conditions for ultradifferentiability: a uniform approach
David Nicolas Nenning, Armin Rainer, Gerhard Schindl
Recent work showed that a theorem of Joris (that a function is smooth if two coprime powers of are smooth) is valid in a wide variety of ultradifferentiable classes $\mathc…
Nonlinear conditions for ultradifferentiability
David Nicolas Nenning, Armin Rainer, Gerhard Schindl
A remarkable theorem of Joris states that a function is if two relatively prime powers of are . Recently, Thilliez showed that an analogous theorem hol…
Roots of Garding hyperbolic polynomials
Armin Rainer
We explore the regularity of the roots of Garding hyperbolic polynomials and real stable polynomials. As an application we obtain new regularity results of Sobolev type for the eig…
On the extension of Whitney ultrajets of Beurling type
Armin Rainer
We prove a version of Whitney's extension theorem in the ultradifferentiable Beurling setting with controlled loss of regularity. As a by-product we show the existence of continuou…