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A particular type of summability of divergent power series, with an application to difference equations
We define a "weak Borel-sum" for a class of formal power series. This is a generalization of the ordinary Borel-sum with applications in the theory of locally analytic difference equations. We
Accelero-summation of the formal solutions of nonlinear difference equations
In 1996, Braaksma and Faber established the multi-summability, on suitable multi-intervals, of formal power series solutions of locally analytic, nonlinear difference equations, in the absence of
Exact asymptotics of nonlinear difference equations with levels $1$ and $1^+$
On etudie une classe d'equations aux differences finies, non-lineaires, possedants une solution formelle en forme de serie 1-Gevrey qui, en general, n'est pas Borel-sommable. En utilisant des
On the Relation between Global Properties of Linear Difference and Differential Equations with Polynomial Coefficients, II
This paper is the second one in a series of three articles dealing with applications of the Mellin transformation to the theory of linear differential and difference equations with polynomial
Asymptotics of Analytic Difference Equations
Linear difference equations.- Existence proofs for right inverses of difference operators.- Nonlinear difference equations.
On the Relation between Linear Difference and Differential Equations with Polynomial Coefficients
This paper represents the third part of a contribution to the “dictionary” of homogeneous linear differential equations with polynomial coefficients on one hand and corresponding difference equations
Summation of formal solutions of a class of linear difference equations
We consider difference equations y(s+1) = A(s)y(s), where A(s) is an n x n-matrix meromorphic in a neighborhood of infinity with det A(s) not equal 0. In general, the formal fundamental solutions of
Resurgent functions and connections matrices for a linear homogeneous system of difference equations
Soit l'equation y(x+1)=A(x)y(x) ou A∈Gl(N; C{x −1 }), N∈N. Soit A(x)=Σ h=0 ∞ A h x −h . On suppose que A 0 a N valeurs propres distinctes. Cette equation possede une matrice fondamentale formelle de
Existence theorem for nonlinear difference equations
We prove an asymptotic existence theorem for locally analytic, nonlinear difference equations possessing a formal power series solution at infinity. The proof is based on a well-known contraction