25 citations · 63 across the 10 of their papers we have counts for
11 papers
Ultradifferentiable classes of entire functions
David Nicolas Nenning, Gerhard Schindl
We study classes of ultradifferentiable functions defined in terms of small weight sequences violating standard growth and regularity requirements. First, we show that such classes…
On generalized definitions of ultradifferentiable classes
Javier Jiménez-Garrido, David Nicolas Nenning, Gerhard Schindl
We show that the ultradifferentiable-like classes of smooth functions introduced and studied by S. Pilipović, N. Teofanov and F. Tomić are special cases of the general framework of…
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…
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…
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…
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…
Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis
Stefan Fürdös, David Nicolas Nenning, Armin Rainer +1
We review and extend the description of ultradifferentiable functions by their almost analytic extensions, i.e., extensions to the complex domain with specific vanishing rate of th…
On time-dependent Besov vector fields and the regularity of their flows
David Nicolas Nenning
We show ODE-closedness for a large class of Besov spaces , where . ODE-closedness means that…
The Trouvé group for spaces of test functions
David Nicolas Nenning, Armin Rainer
The Trouvé group from image analysis consists of the flows at a fixed time of all time-dependent vectors fields of a given regularity $\mathcal A(\mathbb…
On groups of Hölder diffeomorphisms and their regularity
David Nicolas Nenning, Armin Rainer
We study the set of orientation preserving diffeomorphisms of which differ from the identity by a Hölder -mapping, where $n…