Esterlè's proof of the tauberian theorem for Beurling algebras

Dales, H. G., and Hayman, W. K.. "Esterlè's proof of the tauberian theorem for Beurling algebras." Annales de l'institut Fourier 31.4 (1981): 141-150. <http://eudml.org/doc/74512>.

@article{Dales1981,
abstract = {Recently in this Journal J. Esterlé gave a new proof of the Wiener Tauberian theorem for $L^1(\{\bf R\})$ 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 $L^1_\varphi (\{\bf R\})$. Our estimates need a theorem of Hayman and Korenblum.},
author = {Dales, H. G., Hayman, W. K.},
journal = {Annales de l'institut Fourier},
keywords = {Ahlfors-Heins theorem; bounded analytic functions; Beurling algebras},
language = {eng},
number = {4},
pages = {141-150},
publisher = {Association des Annales de l'Institut Fourier},
title = {Esterlè's proof of the tauberian theorem for Beurling algebras},
url = {http://eudml.org/doc/74512},
volume = {31},
year = {1981},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 31
IS - 4
SP - 141
EP - 150
AB - Recently in this Journal J. Esterlé gave a new proof of the Wiener Tauberian theorem for $L^1({\bf R})$ 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 $L^1_\varphi ({\bf R})$. Our estimates need a theorem of Hayman and Korenblum.
LA - eng
KW - Ahlfors-Heins theorem; bounded analytic functions; Beurling algebras
UR - http://eudml.org/doc/74512
ER -