We consider a free interpolation problem in Nevanlinna and Smirnov classes and find a characterization of the corresponding interpolating sequences in terms of the existence of harmonic majorants of certain functions. We also consider the related problem of characterizing positive functions in the disk having a harmonic majorant. An answer is given in terms of a dual relation which involves positive measures in the disk with bounded Poisson ARTICLE IN PRESS $ (A. Hartmann), xavier@mat.ub.es (X. Massaneda), artur@mat.uab.es (A. Nicolau), pthomas@cict.fr (P. Thomas).

Let Ω be a bounded hyperconvex domain in C n , 0 ∈ Ω, and S ε a family of N poles in Ω, all tending to 0 as ε tends to 0. To each S ε we associate its vanishing ideal I ε and pluricomplex Green function G ε = G Iε . Suppose that, as ε tends to 0, (I ε ) ε converges to I (local uniform convergence), and that (G ε ) ε converges to G, locally uniformly away from 0; then G ≥ G I . If the Hilbert-Samuel multiplicity of I is strictly larger than its length (codimension, equal to N here), then (G ε ) ε cannot converge to G I . Conversely, if I is a complete intersection ideal, then (G ε ) ε converges to G I . We work out the case of three poles.