Un théorème de type Beurling–Lax dans la boule unité

Alpay, Daniel; Dijksma, Aad; Rovnyak, James

Comptes Rendus. Mathématique, Tome 334 (2002) no. 5, pp. 349-354.

Nous démontrons un théorème de type Beurling–Lax pour une famille d'espaces de Hilbert à noyau reproduisant dont les éléments sont des fonctions analytiques dans un sous ensemble ouvert de la boule unité qui contient l'origine. Ces espaces sont caractérisés par des fonctions appelées multiplicateurs de Schur. Nous utilisons la théorie des relations linéaires dans les espaces de Pontryagin pour donner une réalisation coisométrique pour les multiplicateurs de Schur.

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.

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