ABSTRACT
In his monograph "Le Operazioni Distributive e le loro Applicazioni all’Analisi", Salvatore Pincherle considered in a systematic way different linear operators in spaces of analytic functions. Among them he emphasized the consideration of the process of analytic continuation as an operator, inducing a representation of the homotopy group of the domain. In particular, it becomes natural to consider functional equations involving this operator. J. Ecalle's theory of the resurgent functions could be considered as an attempt to develop an algebraic theory of the operators of analytic continuation. This chapter mentions one of them, the author's joint work with Ahmed Sebbar on an old problem of A. Hurwitz.
