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Some algebraic properties of the Wiener-Laplace algebra
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2010 (English)In: Journal of Applied Analysis, ISSN 1425-6908, Vol. 16, no 1, 79-94 p.Article in journal (Refereed) Published
Abstract [en]

We denote by W +(ℂ +) the set of all complex-valued functions defined in the closed right half plane ℂ + D {s ∈ ℂ | Re(s) ≥ 0} that differ from the Laplace transform of functions from L 1(0, ∞) by a constant. Equipped with pointwise operations, W +(C +) forms a ring. It is known that W +(ℂ +) is a pre-Bézout ring. The following properties are shown for W +(ℂ +): W +(ℂ +) is not a GCD domain, that is, there exist functions F 1, F 2 in W +(ℂ +) that do not possess a greatest common divisor in W +(ℂ +). W +(ℂ +) is not coherent, and in fact, we give an example of two principal ideals whose intersection is not finitely generated. We will also observe that W +(ℂ +) is a Hermite ring, by showing that the maximal ideal space of W +(ℂ +), equipped with the Gelfand topology, is contractible.

Place, publisher, year, edition, pages
2010. Vol. 16, no 1, 79-94 p.
Keyword [en]
Control theory, GCD domain, Wiener-Laplace algebra
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-150335DOI: 10.1515/JAA.2010.006Scopus ID: 2-s2.0-84858422146OAI: oai:DiVA.org:kth-150335DiVA: diva2:742435
Note

QC 20140901

Available from: 2014-09-01 Created: 2014-09-01 Last updated: 2014-09-01Bibliographically approved

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  • apa
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  • Other locale
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