20 citations · 86 across the 50 of their papers we have counts for
24 papers · 1 filter
Formal solution and strong asymptotic expansion of some initial value problem in two complex time variables, infinite order irregular singularities and Mahler transforms
Alberto Lastra, Stephane Malek
A formal solution to a partial differential equation of infinite order involving the action of Mahler-type operators in several variables is obtained. Such formal solutions is cons…
On some -analog of an initial value problem with infinite order irregular singularity and Mahler transforms
Alberto Lastra, Stephane Malek
A family of -difference-differential equations in two complex variables is studied, under the action of a so-called Mahler transform on time variable. The appearance of a leadin…
Parametric formal Gevrey asymptotic expansions in two complex time variable problems
Guoting Chen, Alberto Lastra, Stephane Malek
The analytic and formal solutions to a family of singularly perturbed partial differential equations in the complex domain involving two complex time variables are considered. The…
Gevrey versus q-Gevrey asymptotic expansions for some linear q-difference-differential Cauchy problem
Alberto Lastra, Stéphane Malek
The asymptotic behavior of the analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain is studied. Different asymptotic exp…
Meromorphic solutions of linear -difference equations
Alberto Lastra, Pascal Remy
In this article, we construct explicit meromorphic solutions of first order linear -difference equations in the complex domain and we describe the location of all their zeros an…
On q-Gevrey asymptotics for logarithmic type solutions in singularly perturbed q-difference-differential equations
Alberto Lastra, Stéphane Malek
A family of singularly perturbed q-difference-differential equations under the action of a small complex perturbation parameter is studied. The action of the formal monodromy aroun…
On conditions determining formal automorphisms of integro-differential operators
Alberto Lastra, Sławomir Michalik, Maria Suwińska
Results providing conditions on a family of integro-differential operators to determine a formal automorphism are established. Equivalently, the problem can be read in terms of exi…
On sequences preserving q-Gevrey asymptotic expansions
Alberto Lastra, Sławomir Michalik
The modification of the coefficients of formal power series is analyzed in order that such variation preserves q-Gevrey asymptotic properties, in particular q-Gevrey asymptotic exp…
Summability of formal solutions for some generalized moment partial differential equations
Alberto Lastra, Slawomir Michalik, Maria Suwinska
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper…
On a analog of a singularly perturbed problem of irregular type with two complex time variables
Alberto Lastra, Stéphane Malek
Analytic solutions and their formal asymptotic expansions for a family of the singularly perturbed difference-differential equations in the complex domain are constructed. They…
Boundary layer expansions for initial value problems with two complex time variables
Alberto Lastra, Stéphane Malek
We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter . We construct inner and outer solutions of the p…
On singularly perturbed linear initial value problems with mixed irregular and Fuchsian time singularities
Alberto Lastra, Stephane Malek
We consider a family of linear singularly perturbed PDE relying on a complex perturbation parameter . As in a former study of the authors (A. Lastra, S. Malek, Parametric Gevrey…
Maillet type theorem for nonlinear totally characteristic partial differential equations
Alberto Lastra, Hidetoshi Tahara
The paper discusses a holomorphic nonlinear singular partial differential equation under the assumpt…
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…
On parametric Gevrey asymptotics for initial value problems with infinite order irregular singularity and linear fractional transforms
Alberto Lastra, Stéphane Malek
This paper is a continuation a previous work of the authors where parametric Gevrey asymptotics for singularly perturbed nonlinear PDEs has been studied. Here, the partial differen…
On parametric Gevrey asymptotics for some initial value problems in two asymmetric complex time variables
Alberto Lastra, Stéphane Malek
We study a family of nonlinear initial value partial differential equations in the complex domain under the action of two asymmetric time variables. Different Gevrey bounds and mul…
On parametric Gevrey asymptotics for some nonlinear initial value problems in two complex time variables
Alberto Lastra, Stephane Malek
The asymptotic behavior of a family of singularly perturbed PDEs in two time variables in the complex domain is studied. The appearance of a multilevel Gevrey asymptotics phenomeno…
Multiscale Gevrey asymptotics in boundary layer expansions for some initial value problem with merging turning points
Alberto Lastra, Stéphane Malek
We consider a nonlinear singularly perturbed PDE leaning on a complex perturbation parameter . The problem possesses an irregular singularity in time at the origin and involves…
On parametric multilevel q-Gevrey asymptotics for some linear Cauchy problem
Alberto Lastra, Stéphane Malek
We study a linear difference-differential Cauchy problem, under the action of a perturbation parameter . This work deals with a analog of the research made in a previoue…
Multi-level Gevrey solutions of singularly perturbed linear partial differential equations
Alberto Lastra, Stéphane Malek
We study the asymptotic behavior of the solutions related to a family of singularly perturbed linear partial differential equations in the complex domain. The analytic solutions ob…
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…