Récemment dans ce Journal J. Esterlé a donné une preuve nouvelle du théorème taubérien de Wiener pour 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 . 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 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 . Our estimates need a theorem of Hayman and Korenblum.
@article{AIF_1981__31_4_141_0, 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}, volume = {31}, year = {1981}, pages = {141-150}, doi = {10.5802/aif.852}, mrnumber = {83j:43007}, zbl = {0449.40005}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_1981__31_4_141_0} }
Dales, H. G.; Hayman, W. K. Esterlè's proof of the tauberian theorem for Beurling algebras. Annales de l'Institut Fourier, Tome 31 (1981) pp. 141-150. doi : 10.5802/aif.852. http://gdmltest.u-ga.fr/item/AIF_1981__31_4_141_0/
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