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Some finite-dimensional backward shift-invariant subspaces in the ball and a related factorization problem

Alpay, D
Kaptanoglu, HT
Beurling's theorem characterizes subspaces of the Hardy space invariant under the forward-shift operator in terms of inner functions. In this Note we consider the case where the ball replaces the open unit desk and the reproducing kernel Hilbert space with reproducing kernel 1/(1-Sigma (N)(1) a(j)w(j)*) replaces the Hardy space. We give explicit formulas which generalize Blaschke products in the case of spaces of finite codimension. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.