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R´ ESUM´ E.—Pour une hyperfonction µ(x )` a support compact, on considere l'´equation de convolution (E) µ ∗ f = g avec des fonctions holomorphes f et g definies sur un domaine de la forme U × √ −1Rn. Sous une condition naturelle, dite condition (S), on demontre l'existence de solution de (E) et le prolongement de solution de l'´equation homogene µ ∗ f =0 . En dl'ensemble caracteristique Char(µ∗), ceci entraˆone que les directions auxquelles une solution ne se prolonge pas sont estimees par Char(µ∗). ABSTRACT. — For a hyperfunction µ(x) with compact support, we consider the convolution equation (E) µ ∗ f = g with holomorphic functions f and g defined on a domain of the form U × √ −1R n . Under a natural condition (the condition (S)), we will prove the existence of solution of (E) and the analytic continuation of homogeneous equation µ∗f = 0. Defining the characteristic set Char(µ∗), these imply that directions to which a solution cannot be continued are estimated by Char(µ∗).

The existence and the continuation of holomorphic solutions for convolution equations in tube domains