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Autour de quelques équations fonctionnelles analytiques

Abstract : This thesis concerns the study of analytic functional equations. It is divided in two parts. The first one deals with mixed q-difference-differential equations. We establish index theorems and growth estimates for entire functions solutions of such equations. The results we obtain extend those established separately for differential equations and for q-difference equations. We also get index theorems for the expansions in q-factorial formal series (q-analogs of factorial series). The second part of the thesis is about a resummation algorithm of formal power series solutions of linear ordinary differential equations in the neighbourhood of an irregular singula-rity, supposed to be located at the origin. This algorithm describes the iterated Borel-Laplace transforms method. On the basis of computer algebra implementations studied in the European working group CATHODE (Computer Algebra Tools for Handling Ordinary Differential Equations) we develop the algorithmic approach of the power series multisummation.
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Fabienne Naegele. Autour de quelques équations fonctionnelles analytiques. Modélisation et simulation. Institut National Polytechnique de Grenoble - INPG, 1995. Français. ⟨tel-00005056⟩

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