62 citations · 389 across the 51 of their papers we have counts for
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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…
On optimal solutions of the Borel problem in the Roumieu case
David Nicolas Nenning, Armin Rainer, Gerhard Schindl
The Borel problem for Denjoy--Carleman and Braun--Meise--Taylor classes has well-known optimal solutions. The unified treatment of these ultradifferentiable classes by means of one…
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…
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…
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…