5 papers
Summability of formal solutions of some singular perturbations problems in differential and moment differential equations
Maria KsiÄ Å¼kiewicz, SÅawomir Michalik
In this paper we study the summability of solutions of some general forms of singularly perturbed linear ordinary differential and moment differential equations. We conclude that u…
Formal power series solutions with coefficients defined on shrinking discs for some partial differential equations
Alberto Lastra, SÅawomir Michalik, Maria SuwiÅska
In this paper conditions, under which an integro-differential operator is a linear automorphism, are provided. Alternatively, the problem can be considered in terms of existence of…
On conditions determining formal automorphisms of integro-differential operators
Alberto Lastra, SÅawomir Michalik, Maria SuwiÅska
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 summability
SÅawomir Michalik, Maria SuwiÅska, Bożena Tkacz
In this paper, we study sequences of positive numbers preserving summability. In particular, the open set property for such a family of sequences is shown. Several classes of seque…
On integral representations of -difference operators and their applications
Antonio Cáceres, Alberto Lastra, SÅawomir Michalik +1
Integral representations of two -difference operators are provided in terms of special functions arising in the theory of asymptotic solutions to -difference equations in the…