38 citations · 160 across the 19 of their papers we have counts for
12 papers · 1 filter
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…
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.…
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…
Ultraholomorphic extension theorems in the mixed setting
Javier Jiménez-Garrido, Javier Sanz, Gerhard Schindl
The aim of this work is to generalize the ultraholomorphic extension theorems from V. Thilliez in the weight sequence setting and from the authors in the weight function setting (o…
Multisummability in Carleman ultraholomorphic classes by means of nonzero proximate orders
Javier Jiménez-Garrido, Shingo Kamimoto, Alberto Lastra +1
We introduce a general multisummability theory of formal power series in Carleman ultraholomorphic classes. The finitely many levels of summation are determined by pairwise compara…
Injectivity and surjectivity of the asymptotic Borel map in Carleman ultraholomorphic classes
Javier Jiménez-Garrido, Javier Sanz, Gerhard Schindl
We study the injectivity and surjectivity of the Borel map in three instances: in Roumieu-Carleman ultraholomorphic classes in unbounded sectors of the Riemann surface of the logar…
A Phragmén-Lindelöf theorem via proximate orders, and the propagation of asymptotics
Javier Jiménez-Garrido, Javier Sanz, Gerhard Schindl
We prove that, for asymptotically bounded holomorphic functions in a sector in , an asymptotic expansion in a single direction towards the vertex with constraints in te…
Flat functions in Carleman ultraholomorphic classes via proximate orders
Javier Sanz
Whenever the defining sequence of a Carleman ultraholomorphic class (in the sense of H. Komatsu) is strongly regular and associated with a proximate order, flat functions are const…
Summability in general Carleman ultraholomorphic classes
Alberto Lastra, Stephane Malek, Javier Sanz
A definition of summability is put forward in the framework of general Carleman ultraholomorphic classes in sectors, so generalizing summability theory as developed by J.-P. Ra…
Continuous right inverses for the asymptotic Borel map in ultraholomorphic classes via a Laplace-type transform
Alberto Lastra, Stéphane Malek, Javier Sanz
A new construction of linear continuous right inverses for the asymptotic Borel map is provided in the framework of general Carleman ultraholomorphic classes in narrow sectors. Suc…
Strong asymptotic expansions in a multidirection
Alberto Lastra, Jorge Mozo-Fernández, Javier Sanz
In this paper we prove that, for asymptotically bounded holomorphic functions defined in a polysector in , the existence of a strong asymptotic expansion in Majima's…
Quasi-analyticity in Carleman ultraholomorphic classes
Alberto Lastra, Javier Sanz
We give a characterization for two different concepts of quasi-analyticity in Carleman ultraholomorphic classes of functions of several variables in polysectors. Also, working with…