28 citations · 130 across the 22 of their papers we have counts for
23 papers
Sequences of generalized moments and their applications to some moment partial differential equations
Sławomir Michalik, Hiroshi Yamazawa
We introduce sequences of generalized moments that are a generalization of sequences preserving summability and sequences of moments from Balser's theory of moment summability. We…
Summability of formal solutions of some singular perturbations problems in differential and moment differential equations
Maria Książkiewicz, Sławomir 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, Sławomir Michalik, Maria Suwińska
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 sequences preserving summability
Sławomir Michalik, Maria Suwińska, 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, Sławomir 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…
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…
On the summability and convergence of formal solutions of linear -difference-differential equations with constant coefficients
Kunio Ichinobe, Sławomir Michalik
We consider the Cauchy problem for homogeneous linear -difference-differential equations with constant coefficients. We characterise convergent, -summable and multisummable f…
On polyharmonic polynomials
Hubert Grzebuła, Sławomir Michalik
We study the orthogonal projection of homogeneous polynomials onto the space of homogeneous polyharmonic polynomials. To do this we derive the decomposition of homogeneous polynomi…
Multisummability of formal solutions for a family of generalized singularly perturbed moment differential equations
Alberto Lastra, Sławomir Michalik, Maria Suwińska
The notion of moment differentiation is extended to the set of generalized multisums of formal power series via an appropriate integral representation and accurate estimates of the…
Summable solutions of the Goursat problem for some partial differential equations with constant coefficients
Sławomir Michalik
We consider the Goursat problem for linear partial differential equations with constant coefficients in two complex variables. We find the conditions for summable solutions of the…
Summability of formal solutions for a family of generalized moment integro-differential equations
Alberto Lastra, Sławomir Michalik, Maria Suwińska
Generalized summability results are obtained regarding formal solutions of certain families of linear moment integro-differential equations with time variable coefficients. The mai…
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…
Estimates of formal solutions for some generalized moment partial differential equations
Alberto Lastra, Sławomir Michalik, Maria Suwińska
Using increasing sequences of real numbers, we generalize the idea of formal moment differentiation first introduced by W. Balser and M. Yoshino. Slight departure from the concept…
Gevrey estimates for certain moment partial differential equations
Sławomir Michalik, Maria Suwińska
We consider the Cauchy problem for inhomogeneous linear moment differential equations with holomorphic time dependent coefficients. Using such tools as the formal norms, theory of…
The Stokes phenomenon for some moment partial differential equations
Sławomir Michalik, Bożena Tkacz
We study the Stokes phenomenon for the solutions of general homogeneous linear moment partial differential equations with constant coefficients in two complex variables under condi…
Hyperasymptotic solutions for certain partial differential equations
Sławomir Michalik, Maria Suwińska
We present the hyperasymptotic expansions for a certain group of solutions of the heat equation. We extend this result to a more general case of linear PDEs with constant coefficie…
Spherical polyharmonics and Poisson kernels for polyharmonic functions
Hubert Grzebuła, Sławomir Michalik
We introduce and develop the notion of spherical polyharmonics, which are a natural generalisation of spherical harmonics. In particular we study the theory of zonal polyharmonics,…
A Dirichlet type problem for complex polyharmonic functions
Hubert Grzebuła, Sławomir Michalik
We extend holomorphically polyharmonic functions on a real ball to a complex set being the union of rotated balls. We solve a Dirichlet type problem for complex polyharmonic functi…
The Stokes phenomenon for certain partial differential equations with meromorphic initial data
Sławomir Michalik, Bożena Podhajecka
We study the Stokes phenomenon for the solutions of the 1-dimensional complex heat equation and its generalizations with meromorphic initial data. We use the theory of Borel summab…
Analytic and summable solutions of inhomogeneous moment partial differential equations
Sławomir Michalik
We study the Cauchy problem for a general inhomogeneous linear moment partial differential equation of two complex variables with constant coefficients, where the inhomogeneity is…
Summable solutions of some partial differential equations and generalised integral means
Sławomir Michalik
We describe partial differential operators for which we can construct generalised integral means satisfying Pizzetti-type formulas. Using these formulas we give a new characterisat…
Summability of formal solutions of linear partial differential equations with divergent initial data
Sławomir Michalik
We study the Cauchy problem for a general homogeneous linear partial differential equation in two complex variables with constant coefficients and with divergent initial data. We s…