Un théorème de type Beurling–Lax dans la boule unité

We prove a Beurling-Lax theorem for a family of reproducing kernel Hilbert spaces of functions analytic in an open subset of the unit ball containing the origin. The spaces under consideration are characterized by functions called Schur multipliers. Using the theory of linear relations in Pontryagin spaces we also give coisometric realizations of Schur multipliers. To cite this article: D. Alpay et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 349-354.  2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS