On the spectra and invertibility of certain operators in systems theory
Tannenbaum, Allen R.
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In this paper we study the following kind of problem. Let T be an arbitrary contraction. We will define a certain function which will lead to an explicit procedure for the computation of the isolated spectrum of w(T)w(T)', T any contraction. We will then show how this generalizes the results of [l-31. (See (2.1) and (2.2) below.) We will moreover apply our theory to operators TϵC.₀ and in particular derive a relatively simple expression for the calculation of the discrete spectrum of w (T). We should note that from the control engineering point of view, this means that one can now solve an important special case of the general model-matching problem discussed in [SI for multivariate distributed systems as a well as treat a whole new range of Hankel norm approximation problems. We plan to return to these topics in a future applications oriented paper.