Linear Systems and Higher Order Equations

Abstract

Definition 5.1. Let A be an m × n-matrix-valued function on $\mathbb{T}$. We say that A is rd-continuous on $\mathbb{T}$ if each entry of A is rd-continuous $\mathbb{T}$ , and the class of all such rd-continuous onm × n-matrix-valued functions on $\mathbb{T}$ is denoted, similar to the scalar case (see Definition 1.58), by

$$ C_{rd} = C_{rd} (\mathbb{T}) = C_{rd} (\mathbb{T},\mathbb{R}^{m \times n} ). $$