An inverse spectral problem for rational matrix functions and minimal divisibility
Copyright policy )An inverse spectral problem for rational matrix functions and minimal divisibility
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)].
- Tel Aviv University Israel
- Vrije Universiteit Amsterdam Netherlands
local spectral data, inverse spectral theorem, Matrices over function rings in one or more variables, minimal divisibility theorem, Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators, regular rational matrix functions, Spectrum, resolvent, Pole and zero placement problems, Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
local spectral data, inverse spectral theorem, Matrices over function rings in one or more variables, minimal divisibility theorem, Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators, regular rational matrix functions, Spectrum, resolvent, Pole and zero placement problems, Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
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