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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. WeExpand
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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 ofExpand
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ON THE RELATION BETWEEN GLOBAL PROPERTIES OF LINEAR DIFFERENCE AND DIFFERENTIAL-EQUATIONS WITH POLYNOMIAL COEFFICIENTS .1.
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 polynomialExpand
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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 desExpand
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Asymptotics of Analytic Difference Equations
Linear difference equations.- Existence proofs for right inverses of difference operators.- Nonlinear difference equations.
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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 equationsExpand
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The Stokes phenomenon and Hilbert's 16th problem, Groningen, The Netherlands, 31 May - 3 June 1995
Non-accumulation of limit cycles - revisiting and simplyifyng a former proof followed by construction of a summit-crossing "central trajectory" at semihyperbolic points, J. Ecalle finiteness theoremsExpand
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A NOTE ON THE RELATIONSHIP BETWEEN STOKES MULTIPLIERS AND FORMAL SOLUTIONS OF ANALYTIC DIFFERENTIAL-EQUATIONS
This paper generalizes a result of Balser, Jurkat, and Lutz [J. Math. Anal. Appl., 71 (1979), pp. 48–94] concerning the relation between the Stokes multipliers of a homogeneous linear differentialExpand
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The Stokes phenomenon in exact asymptotics
As an introduction we present a new, elementary and constructive proof of the multisummability properties of formal solutions of linear ODE's at irregular singular points. This serves to illustrateExpand
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