Minimal Nodes

Abstract

In this chapter the notion of a minimal node is considered. If two nodes are similar, then they have the same transfer function. The converse statement is not true. In fact nodes with rather different state spaces may have the same transfer function. For minimal nodes this phenomenon does not occur. In Section 3.1 minimal nodes are defined. In the finite dimensional case the connection between a minimal node 6 and its transfer function W_θ is very close. For example in that case 9 is determined up to similarity by W_θ. Also in that case the poles and zeros of W_θ . determine completely the eigenvalue structure of the main operator and associate main operator of 6, respectively. This will be explained in Section 3–2. In Section 3.3 the notion of minimality is considered for Brodskii nodes, Krein nodes, monic nodes and polynomial nodes.