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On the Krull Dimension of Rings of Transfer Functions

On the Krull Dimension of Rings of Transfer Functions In this article, we prove that the Krull dimension of several commonly used classes of transfer functions of infinite dimensional linear control systems is infinite. On the other hand, we also show that the weak Krull dimension of the Hardy algebra $H^{\infty}(\mathbb{D})$ , the disk algebra $A(\mathbb{D})$ and the Wiener algebra $W_{+}(\mathbb{D})$ is equal to 1. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

On the Krull Dimension of Rings of Transfer Functions

Acta Applicandae Mathematicae , Volume 103 (2) – Mar 14, 2008

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References (15)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer Science+Business Media B.V.
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-008-9227-1
Publisher site
See Article on Publisher Site

Abstract

In this article, we prove that the Krull dimension of several commonly used classes of transfer functions of infinite dimensional linear control systems is infinite. On the other hand, we also show that the weak Krull dimension of the Hardy algebra $H^{\infty}(\mathbb{D})$ , the disk algebra $A(\mathbb{D})$ and the Wiener algebra $W_{+}(\mathbb{D})$ is equal to 1.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Mar 14, 2008

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