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.
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.
@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}, pages = {141--150}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {31}, number = {4}, year = {1981}, doi = {10.5802/aif.852}, mrnumber = {83j:43007}, zbl = {0449.40005}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.852/} }
TY - JOUR AU - Dales, H. G. AU - Hayman, W. K. TI - Esterlè's proof of the tauberian theorem for Beurling algebras JO - Annales de l'Institut Fourier PY - 1981 SP - 141 EP - 150 VL - 31 IS - 4 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.852/ DO - 10.5802/aif.852 LA - en ID - AIF_1981__31_4_141_0 ER -
%0 Journal Article %A Dales, H. G. %A Hayman, W. K. %T Esterlè's proof of the tauberian theorem for Beurling algebras %J Annales de l'Institut Fourier %D 1981 %P 141-150 %V 31 %N 4 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.852/ %R 10.5802/aif.852 %G en %F 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, Volume 31 (1981) no. 4, pp. 141-150. doi : 10.5802/aif.852. http://www.numdam.org/articles/10.5802/aif.852/
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