62 citations · 390 across the 53 of their papers we have counts for
12 papers · 1 filter
On the equivalence between moderate growth-type conditions in the weight matrix setting II
Gerhard Schindl
We continue the study of the known equivalent reformulations of the classical moderate growth condition for weight sequences in the mixed setting; i.e. when dealing with two differ…
Generalized upper and lower Legendre conjugates for weight functions
Gerhard Schindl
We introduce and study new transformations between two functions satisfying some basic growth properties and generalize the known lower and upper Legendre conjugate (or envelope).…
On the regularization of sequences and associated weight functions
Gerhard Schindl
We revisit and generalize the geometric procedure of regularizing a sequence of real numbers with respect to a so-called regularizing function. This approach was studied by S. Mand…
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…
Surjectivity of the asymptotic Borel map in Carleman-Roumieu ultraholomorphic classes defined by regular sequences
Javier Jiménez-Garrido, Javier Sanz, Gerhard Schindl
We study the surjectivity of, and the existence of right inverses for, the asymptotic Borel map in Carleman-Roumieu ultraholomorphic classes defined by regular sequences in the sen…
On the extension of Whitney ultrajets, II
Armin Rainer, Gerhard Schindl
We characterize the validity of the Whitney extension theorem in the ultradifferentiable Roumieu setting with controlled loss of regularity. Specifically, we show that in the main…
On the extension of Whitney ultrajets
Armin Rainer, Gerhard Schindl
We prove necessary and sufficient conditions for the validity of Whitney's extension theorem in the ultradifferentiable Roumieu setting with controlled loss of regularity.
Log-convex sequences and nonzero proximate orders
Javier Jiménez-Garrido, Javier Sanz, Gerhard Schindl
Summability methods for ultraholomorphic classes in sectors, defined in terms of a strongly regular sequence , have been put forward by A. Last…
Extension of Whitney jets of controlled growth
Armin Rainer, Gerhard Schindl
We revisit Whitney's extension theorem in the ultradifferentiable Roumieu setting. Based on the description of ultradifferentiable classes by weight matrices, we extend results on…
On the Borel mapping in the quasianalytic setting
Armin Rainer, Gerhard Schindl
The Borel mapping takes germs at of smooth functions to the sequence of iterated partial derivatives at . We prove that the Borel mapping restricted to the germs of any quas…
Equivalence of stability properties for ultradifferentiable function classes
Armin Rainer, Gerhard Schindl
We characterize stability under composition, inversion, and solution of ordinary differential equations for ultradifferentiable classes, and prove that all these stability properti…