An inverse spectral problem for rational matrix functions and minimal divisibility (Q1089886)

This paper concerns the study of regular rational matrix functions in terms of their local spectral data. A concise account is given of the main ideas and recent results in this area. In particular, the paper gives short and selfcontained proofs of an inverse spectral theorem of \textit{J. A. Ball} and \textit{A. C. M. Ran}, ibid. 10, 349-415 (1987; review above) and of the minimal divisibility theorem due to \textit{I. Gohberg, M. A. Kaashoek, L. Lerer} and \textit{L. Rodman} [in: Operator Theory, Adv. Appl. 12, 241-275 (1984; Zbl 0541.47012)].