J-inner matrix functions, interpolation and inverse problems for canonicalsystems, III: More on the inverse monodromy problem

This paper is a continuation of our sturdy of the inverse monodromy problem for canonical systems of integral and differential equations which appeare d in a recent issue of this journal. That paper established a parametrizati on of the set of all solutions to the inverse monodromy for canonical integ ral systems in terms of two continuous chains of matrix valued inner functi ons in the special case that the monodromy matrix was strongly regular (and the signature matrix J was not definite). The correspondence between the c hains and the solutions of this monodromy problem is one to one and onto. I ri this paper we study the solutions of this inverse problem for several di fferent classes of chains which are specified by imposing assorted growth c onditions and symmetries on the monodromy matrix and/or the matrizant (i.e. , the fundamental solution) of the underlying equation. These external cond itions serve to either fix or limit the class of admissible chains without computing them explicitly. This is useful because typically the chains are not easily accessible.