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arXiv · 1311.6416

An analytic proof of the Malgrange-Sibuya theorem on the convergence of formal solutions of an ODE

R. R. Gontsov·I. V. Goryuchkina
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Abstract

We propose an analytic proof of the Malgrange-Sibuya theorem concerning a sufficient condition of the convergence of a formal power series satisfying an ordinary differential equation. The proof is based on the majorant method and allows to estimate the radius of convergence of such a series.

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R. R. Gontsov, I. V. Goryuchkina. 2013-11-25. An analytic proof of the Malgrange-Sibuya theorem on the convergence of formal solutions of an ODE. https://arxiv.org/abs/1311.6416

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