Constructive Borel-Ritt interpolation results for functions of several variables

We give constructive proofs for two Borel-Ritt interpolation results, stating the existence of holomorphic functions on polysectors admitting an arbitrarily prescribed asymptotic expansion, whether in the sense of Gerard-Sibuya or in that of Majima. As a consequence, a new proof is obtained for the classical Borel's theorem on the existence of C-infinity functions on R-n with given derivatives at 0; in fact, our construction provides functions analytic in (R-{0})(n).