Sur les équations fonctionnelles auxq-différences

  title={Sur les {\'e}quations fonctionnelles auxq-diff{\'e}rences},
  author={Jean-Paul B{\'e}zivin},
  journal={aequationes mathematicae},
SummaryIn this paper, we study the convergence of formal power series solutionsψ of functional equations of the form∑Pk(xψ)(ϕ[k](x))=θ(x), whereϕ[k](x) denotes thek-th iterate of the functionϕ.We obtain results similar to the results of Malgrange and Ramis for formal solutions of differential equations: ifϕ(0) = 0, andϕ′(0) =q is a nonzero complex number with absolute value less than one then, ifψ(x)=∑a(n)xn is a divergent solution, there exists a positive real numbers such that the power… Expand
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