Corpus ID: 125818219

Sur les 6quations fonctionnelles aux q-diff6rences

  title={Sur les 6quations fonctionnelles aux q-diff6rences},
  author={J. Zivin},
Summary. In this paper, we study the convergence of formal power series solutions ~ of functional equations of the form ~ Pk(X)~b(q~lk~(x)) = O(X), where t, olkl(x) denotes the k-th iterate of the function ~. We obtain results similar to the results of Malgrange and Ramis for formal solutions of differemial equations: if ~p(0) = 0, and q~'(0) = q is a nonzero complex number with absolute value less than one then, if ~p(x) = ~ a(n)x" is a divergent solution, there exists a positive real number s… Expand