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The space of bounded analytic functions on a region

Lee A. RubelA. L. Shields — 1966

Annales de l'institut Fourier

L’espace des fonctions analytiques bornées sur une région peut être muni de plusieurs topologies différentes. Deux topologies faibles sont étudiées ici. L’une est celle appelée topologie stricte et l’autre la topologie faible étoilée. Le principal outil nouveau est une espèce de balayage ou ramonage.

Cyclic vectors and invariant subspaces for the backward shift operator

R. G. DouglasH. S. ShapiroA. L. Shields — 1970

Annales de l'institut Fourier

The operator U of multiplication by z on the Hardy space H 2 of square summable power series has been studied by many authors. In this paper we make a similar study of the adjoint operator U * (the “backward shift”). Let K f denote the cyclic subspace generated by f ( f H 2 ) , that is, the smallest closed subspace of H 2 that contains { U * n f } ( n 0 ) . If K f = H 2 , then f is called a cyclic vector for U * . Theorem : f is a cyclic vector if and only if there is a function g , meromorphic and of bounded Nevanlinna characteristic...

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