ON THE PRE-B ´ EZOUT PROPERTY OF WIENER ALGEBRAS ON THE DISC AND THE HALF-PLANE

Raymond Mortini, Amol Sasane
2008 NEW ZEALAND JOURNAL OF MATHEMATICS   unpublished
Let D denote the open unit disk {z ∈ C | |z| < 1}, and C + denote the closed right half-plane {s ∈ C | Re(s) ≥ 0}. (1) Let W + (D) be the Wiener algebra of the disc, that is the set of all absolutely convergent Taylor series in the open unit disk D, with pointwise operations. (2) Let W + (C +) be the set of all functions defined in the right half-plane C + that differ from the Laplace transform of a function fa ∈ L 1 (0, ∞) by a constant. Equipped with pointwise operations, W + (C +) forms a
more » ... + (C +) forms a ring. We show that the rings W + (D) and W + (C +) are pre-Bézout rings.
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