62 citations · 390 across the 53 of their papers we have counts for
56 papers
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…
Stability under product and composition for uniform Carleman asymptotic expansions
Javier Jiménez-Garrido, Ignacio Miguel-Cantero, Javier Sanz +1
We study the stability under point-wise product and under composition in Carleman classes of holomorphic functions, defined on sectors of the Riemann surface of the logarithm, and…
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…
Surjectivity of the asymptotic Borel map in Carleman ultraholomorphic classes defined by sequences with shifted moments
Javier Jiménez-Garrido, Ignacio Miguel-Cantero, Javier Sanz +1
We prove several improved versions of the Borel-Ritt theorem about the surjectivity of the asymptotic Borel mapping in classes of functions with -uniform asymptotic…
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 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…
On the class of almost subadditive weight functions
Gerhard Schindl
We answer a question from A. V. Abanin and P. T. Tien about so-called almost subadditive weight functions in the sense of Braun-Meise-Taylor. Using recent knowledge of a growth ind…
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…
Stability properties of ultraholomorphic classes of Roumieu-type defined by weight matrices
Javier Jiménez-Garrido, Ignacio Miguel-Cantero, Javier Sanz +1
We characterize several stability properties, such as inverse or composition closedness, for ultraholomorphic function classes of Roumieu type defined in terms of a weight matrix.…
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…
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…
Ellipticity and the problem of iterates in Denjoy-Carleman classes
Stefan Fürdös, Gerhard Schindl
In 1978 Métivier showed that a differential operator with analytic coefficients is elliptic if and only if the theorem of iterates holds for with respect to any non-analyti…
On inclusion relations between weighted spaces of entire functions
Gerhard Schindl
We characterize the inclusions of weighted classes of entire functions in terms of the defining weights resp. weight systems. First we treat weights defined in terms of a so-called…
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…
Optimal flat functions in Carleman-Roumieu ultraholomorphic classes in sectors
Javier Jiménez-Garrido, Ignacio Miguel-Cantero, Javier Sanz +1
We construct optimal flat functions in Carleman-Roumieu ultraholomorphic classes associated to general strongly nonquasianalytic weight sequences, and defined on sectors of suitabl…