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

Recently in this Journal J. Esterlé gave a new proof of the Wiener Tauberian theorem for L 1 (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 L ϕ 1 (R). Our estimates need a theorem of Hayman and Korenblum.

Récemment dans ce Journal J. Esterlé a donné une preuve nouvelle du théorème taubérien de Wiener pour L 1 (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 L ϕ 1 (R). Nos évaluations ont besoin d’un théorème de Hayman et Korenblum.

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     author = {Dales, H. G. and Hayman, W. K.},
     title = {Esterl\`e's proof of the tauberian theorem for {Beurling} algebras},
     journal = {Annales de l'Institut Fourier},
     pages = {141--150},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {31},
     number = {4},
     year = {1981},
     doi = {10.5802/aif.852},
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     mrnumber = {83j:43007},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.852/}
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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

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