Abstract and Applied Analysis

Noncoherence of a Causal Wiener Algebra Used in Control Theory

Amol Sasane

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Abstract

Let 0 : = { s Re ( s ) 0 } , and let 𝒲 + denote the ring of all functions f : 0 such that f ( s ) = f a ( s ) + k = 0 f k e s t k ( s 0 ) , where f a L 1 ( 0 , ) , ( f k ) k 0 1 , and 0 = t 0 < t 1 < t 2 < equipped with pointwise operations. (Here ^ denotes the Laplace transform.) It is shown that the ring 𝒲 + is not coherent, answering a question of Alban Quadrat. In fact, we present two principal ideals in the domain 𝒲 + whose intersection is not finitely generated.

Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 459310, 13 pages.

Dates
First available in Project Euclid: 9 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1220969179

Digital Object Identifier
doi:10.1155/2008/459310

Mathematical Reviews number (MathSciNet)
MR2429624

Zentralblatt MATH identifier
1159.46032

Citation

Sasane, Amol. Noncoherence of a Causal Wiener Algebra Used in Control Theory. Abstr. Appl. Anal. 2008 (2008), Article ID 459310, 13 pages. doi:10.1155/2008/459310. https://projecteuclid.org/euclid.aaa/1220969179


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