Esterlè's proof of the tauberian theorem for Beurling algebras
Annales de l'Institut Fourier, Tome 31 (1981) no. 4, pp. 141-150.

Récemment dans ce Journal J. Esterlé a donné une preuve nouvelle du théorème taubérien de Wiener pour L1(R) en utilisant le théorème de Ahlfors-Heins pour les fonctions analytiques bornées sur un demi-plan. Ici nous utilisons essentiellement la même méthode pour certaines algèbres de Beurling Lϕ1(R). Nos évaluations ont besoin d’un théorème de Hayman et Korenblum.

Recently in this Journal J. Esterlé gave a new proof of the Wiener Tauberian theorem for L1(R) using the Ahlfors-Heins theorem for bounded analytic functions on a half-plane. We here use essentially the same method to prove the analogous result for Beurling algebras Lϕ1(R). Our estimates need a theorem of Hayman and Korenblum.

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     title = {Esterl\`e's proof of the tauberian theorem for {Beurling} algebras},
     journal = {Annales de l'Institut Fourier},
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Dales, H. G.; Hayman, W. K. Esterlè's proof of the tauberian theorem for Beurling algebras. Annales de l'Institut Fourier, Tome 31 (1981) no. 4, pp. 141-150. doi : 10.5802/aif.852. https://www.numdam.org/articles/10.5802/aif.852/

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