1. I am very indebted toV. Glaser, for having communicated to me, already in the spring of 1961, the results that are used here.
2. K. Simanzik:Journ. Math. Phys.,1, 249 (1960).
3. The proof of this result is easy starting from a preliminary theorem that has already been published:L. Bros andV. Glaser:L’enveloppe d’holomorphie de l’union de deux polycercles, preprint. The domain obtained byGlaser is a natural domain of holomorphism. We do not give here the proof of this statement because it is not so immediate and actually we do not need it.
4. In this connectionV. Glaser has actually investigated the most general analytic automorphysm of the tubesT + orT − (private communication).
5. The exact meaning of this requirement and the proof of the statement may be found together with the literature inH. Epstein:Journ. Math. Phys.,1, 524 (1960).