62 citations · 390 across the 53 of their papers we have counts for
31 papers · 1 filter
On equivalent reformulations of condition derivation closedness
Gerhard Schindl
We provide a detailed study of equivalent reformulations of the classical condition derivation closedness for weight sequences. This property is crucial in many applications since…
On convolved weight matrices and local solvability with controlled loss of regularity
Gerhard Schindl
We introduce the convolution between abstractly given anisotropic weight matrices and investigate properties of this new construction. Further, we apply the knowledge to the partic…
The Stieltjes moment problem in Gelfand-Shilov spaces defined by weight sequences in the absence of derivation closedness
Javier Jiménez-Garrido, Ignacio Miguel-Cantero, Javier Sanz +1
The Stieltjes moment problem is studied in a new framework within the general Gelfand-Shilov spaces defined via weight sequences. The novelty consists of allowing for a naturally l…
On the conjugate weight function and ultradifferentiable classes of entire functions
Gerhard Schindl
We introduce the new notion of a conjugate weight function and provide a detailed study of this operation and its properties. Then we apply this knowledge to study classes of ultra…
On inclusion relations of weighted -type spaces defined in terms of weight function matrices
Gerhard Schindl
We introduce new weighted -type spaces defined in terms of weight function matrices and characterize the inclusion relations in terms of the defining matrices. Moreover, we pr…
Generalized upper and lower Legendre conjugates for Braun-Meise-Taylor weight functions
Gerhard Schindl
We apply recent knowledge and techniques of the new generalized upper and lower Legendre conjugates to the theory of weight functions in the sense of Braun-Meise-Taylor and study i…
On the inclusion relations of global ultradifferentiable classes defined by weight matrices
Chiara Boiti, David Jornet, Alessandro Oliaro +1
We study and characterize the inclusion relations of global classes in the general weight matrix framework in terms of growth relations for the defining weight matrices. We conside…
On strong growth conditions for weighted spaces of entire functions
Gerhard Schindl
We characterize the inclusion relations between weighted classes of entire functions with rapid decreasing growth and study strong growth comparison relations between given weights…
Construction of the log-convex minorant of a sequence
Chiara Boiti, David Jornet, Alessandro Oliaro +1
We give a simple construction of the log-convex minorant of a sequence and consequently extend to the -dimensional case the well-known formula tha…
Interpolation of derivatives and ultradifferentiable regularity
Armin Rainer, Gerhard Schindl
Interpolation inequalities for functions allow to bound derivatives of intermediate order by bounds for the derivatives of order and . We review various inte…
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 Orlicz classes defined in terms of associated weight functions
Gerhard Schindl
N-functions and their growth and regularity properties are crucial in order to introduce and study Orlicz classes and Orlicz spaces. We consider N-functions which are given in term…
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 the equivalence between moderate growth-type conditions in the weight matrix setting
Gerhard Schindl
We study the generalizations of the known equivalent reformulations of condition moderate growth from the single weight sequence to the weight matrix setting. This condition, also…
Equality of ultradifferentiable classes by means of indices of mixed O-regular variation
Javier Jiménez-Garrido, Javier Sanz, Gerhard Schindl
We characterize the equality between ultradifferentiable function classes defined in terms of abstractly given weight matrices and in terms of the corresponding matrix of associate…
On subadditivity-like conditions for associated weight functions
Gerhard Schindl
The aim of this article is to provide characterizations for subadditivity-like growth conditions for the so-called associated weight functions in terms of the defning weight sequen…
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…
On the maximal extension in the mixed ultradifferentiable weight sequence setting
Gerhard Schindl
For the ultradifferentiable weight sequence setting it is known that the Borel map which assigns to each function the infinite jet of derivatives (at 0) is surjective onto the corr…
Solid hulls and cores of classes of weighted entire functions defined in terms of associated weight functions
Gerhard Schindl
In the spirit of very recent articles by J. Bonet, W. Lusky and J. Taskinen we are studying the so-called solid hulls and cores of spaces of weighted entire functions when the weig…
Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting
Chiara Boiti, David Jornet, Alessandro Oliaro +1
We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine…
On the construction of large Algebras not contained in the image of the Borel map
Céline Esser, Gerhard Schindl
The Borel map takes germs at 0 of smooth functions to the sequence of iterated partial derivatives at 0. It is well known that the restriction of to the g…
Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis
Chiara Boiti, David Jornet, Alessandro Oliaro +1
We use techniques from time-frequency analysis to show that the space of rapidly decreasing -ultradifferentiable functions is nuclear for every weight function $ω…
The surjectivity of the Borel mapping in the mixed setting for ultradifferentiable ramification spaces
Javier Jiménez-Garrido, Javier Sanz, Gerhard Schindl
We consider r-ramification ultradifferentiable classes, introduced by J. Schmets and M. Valdivia in order to study the surjectivity of the Borel map, and later on also exploited by…