On the Krull Dimension of Rings of Transfer Functions

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.