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

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Current revision

New Zealand Journal of Mathematics

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

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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

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Abstract Let denote the open unit disk { z | |z| < 1 }, and denote the closed right half-plane { s | Re(s) }.

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

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

We show that the rings W ⁺ and W ⁺ are pre-Bézout rings.

Keywords pre-Bézout ring, Wiener algebra

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

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