On the Pre-Bézout Property of Wiener Algebras on the Disc and the Half-Plane

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London School of Economics London School of Economics
-Houghton Street, London WC2A 2AE+Houghton Street
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 +London WC2A 2AE
UNITED KINGDOM UNITED KINGDOM
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|Affiliation3= |Affiliation3=
-|Abstract=+|Abstract={{Abstract - Mortini, Sasane, On the Pre-Bézout Property of Wiener Algebras on the Disc and the Half-Plane}}
-|Keywords=+|Keywords=pre-Bézout ring, Wiener algebra
|Classification= Primary: 30H05; Secondary: 42A99, 93D15 |Classification= Primary: 30H05; Secondary: 42A99, 93D15
|pdf File=[[Media: On the Pre-Bézout Property of Wiener Algebras on the Disc and the Half-Plane.pdf | Full paper]] |pdf File=[[Media: On the Pre-Bézout Property of Wiener Algebras on the Disc and the Half-Plane.pdf | Full paper]]
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Current revision

New Zealand Journal of Mathematics

Vol. 38, (2008), Pages 45-55


R. Mortini

Université Paul Verlaine - Metz

LMAM et Département de Mathématiques

Ile du Saulcy

F-57045 METZ

FRANCE

mailto:mortini@univ-metz.fr

A. Sasane

Mathematics Department

London School of Economics

Houghton Street

London WC2A 2AE

UNITED KINGDOM

mailto:A.J.Sasane@lse.ac.uk




Abstract Let \mathbb{D} denote the open unit disk { z \in \mathbb{C}| |z| < 1 }, and \mathbb{C}_+ denote the closed right half-plane { s \in \mathbb{C}| Re(s) \ge 0 }.


(1) Let W + \mathbb{(D)} be the Wiener algebra of the disc, that is the set of all absolutely convergent Taylor series in the open unit disk \mathbb{D}, with pointwise operations.

(2) Let W + \mathbb{(C_+)} be the set of all functions defined in the right half-plane \mathbb{C_+} that differ from the Laplace transform of a function fa \in L1(0,\infty) by a constant. Equipped with pointwise operations, W + \mathbb{(C_+)}forms a ring.


We show that the rings W + \mathbb{(D)} and W + \mathbb{(C_+)} are pre-Bézout rings.

Keywords pre-Bézout ring, Wiener algebra

Classification (MSC2000) Primary: 30H05; Secondary: 42A99, 93D15

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