# Esterlè's proof of the tauberian theorem for Beurling algebras

Dales, H.G. and Hayman, W. K. (1981) Esterlè's proof of the tauberian theorem for Beurling algebras. Annales de L'Institut Fourier, 31 (4). pp. 141-150. ISSN 1777-5310

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## 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.

Item Type:
Journal Article
Journal or Publication Title:
Annales de L'Institut Fourier
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2608
Subjects:
Departments:
ID Code:
67662
Deposited By:
Deposited On:
22 Nov 2013 10:32
Refereed?:
Yes
Published?:
Published