Accelero-summation of the formal solutions of nonlinear difference equations

G.K. Immink

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Abstract

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.

Original languageEnglish
Pages (from-to)1-51
Number of pages51
JournalAnnales de L'Institut Fourier
Volume61
Issue number1
DOIs
Publication statusPublished - 2011

Keywords

  • Nonlinear difference equation
  • formal solution
  • accelero-sumrnation
  • quasi-function
  • POWER-SERIES
  • MULTISUMMABILITY
  • SUMMABILITY

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