Le problème de Cauchy linéaire et analytique pour un opérateur holomorphe et un second membre ramifié

Abstract

Asymptotic and exact solutions of a Cauchy problem have been often obtained by means of functions U (x, k_l(x),Chrw(133), k_n(x)) where the k_j are characteristic functions of the differential operator. In this way Y. Hamada constructed ramified solutions of Cauchy problems with ramified data.

Recently he paved the way to new results by choosing U more elaborately; namely he defines U by a suitable Goursat problem, whose solutions have a remarquable analytic continuation; hence analytic continuations of solutions of Cauchy problems.

>I sketchded them last October at the franco-japanese symposium held in Marseille-Luminy. But then only preliminaries were known about the case of a ramified second member. Those preliminaries have been now completed.