J-inner matrix functions, interpolation and inverse problems for canonicalsystems, II: The inverse monodromy problem

This is the second of a planned sequence of papers on inverse problems for canonical systems of differential equations. It is devoted to the inverse m onodromy problem for canonical integral and differential systems. In this p art, which focuses on the case of a diagonal signature matrix J, a parametr ization is obtained of the set of all solutions M(t) for the inverse proble m for integral systems in terms of two chains of entire matrix valued inner functions. Special classes of solutions correspond to special choices of t hese chains. This theme will be elaborated upon further in a third part of this paper which will be published in a subsequent issue of this journal. T here the emphasis will be on symmetries and growth conditions all of which serve to specify or restrict the chains alluded to above, from the outside, so to speak.