A constructive proof of the Beurling-Rudin theorem

Raymond Mortini

Displaying similar documents to “A constructive proof of the Beurling-Rudin theorem”

Closed ideals in certain Beurling algebras, and synthesis of hyperdistributions

J. Esterle (1996)

Studia Mathematica

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Spaces of type $H^{\infty} + C$

Walter Rudin (1975)

Annales de l'institut Fourier

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A simple theorem is proved which states a sufficient condition for the sum ot two closed subspaces of a Banach space to be closed. This leads to several analogues of Sarason’s theorem which states that $H^{\infty} + C$ is a closed subalgebra of $L^{\infty}$ . In these analogues, the unit circle is replaces by other groups, and the unit disc is replaced by polydiscs or by balls in spaces of several complex variables. Sums of closed ideals in Banach algebras are also studied.

The space of bounded analytic functions on a region

Lee A. Rubel, A. L. Shields (1966)

Annales de l'institut Fourier

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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.