Accelero-summation of the formal solutions of nonlinear difference equations

@article{Immink2011AccelerosummationOT,
  title={Accelero-summation of the formal solutions of nonlinear difference equations},
  author={Geertrui Klara Immink},
  journal={Annales de l'Institut Fourier},
  year={2011},
  volume={61},
  pages={1-51}
}
  • G. K. Immink
  • Published 2011
  • Mathematics
  • Annales de l'Institut Fourier
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… 

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