Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Esterlè's proof of the tauberian theorem for Beurling algebras
AU - Dales, H.G.
AU - Hayman, W. K.
PY - 1981
Y1 - 1981
N2 - 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.
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.
U2 - 10.5802/aif.852
DO - 10.5802/aif.852
M3 - Journal article
VL - 31
SP - 141
EP - 150
JO - Annales de L'Institut Fourier
JF - Annales de L'Institut Fourier
SN - 1777-5310
IS - 4
ER -