Accelero-summation of the formal solutions of nonlinear difference equations

G.K. Immink

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9 Citaten (Scopus)
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Samenvatting

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 "level 1(+)". Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains; we prove that, under very general conditions, the formal solution is accelero-summable. Its sum is an analytic solution of the equation, represented asymptotically by the formal solution in a certain unbounded domain.

Originele taal-2English
Pagina's (van-tot)1-51
Aantal pagina's51
TijdschriftAnnales de L'Institut Fourier
Volume61
Nummer van het tijdschrift1
DOI's
StatusPublished - 2011

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