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An inverse spectral problem for rational matrix functions and minimal divisibility

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Abstract

The present paper serves as an introduction to the papers [BR 2], [BGR] and [GKLR]. For rational matrix functions a concise account is given of the recent results about inverse spectral problems and minimal divisibility appearing in these three papers.

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References

  • [BGR] Ball, J. A., Gohberg, I., Rodman, L.: Minimal factorization of meromorphic matrix functions in terms of local data, Integral Equations and Operator Theory, this issue.

  • [BR 1] Ball, J. A., Ran, A. C. M.: Global inverse spectral problems for rational matrix functions, Linear Algebra Appl., to appear.

  • [BR 2] Ball, J. A., Ran, A. C. M.: Local inverse spectral problems for rational matrix functions, Integral Equations and Operator Theory, this issue.

  • [BGK] Bart, H., Gohberg, I., Kaashoek, M. A.: Minimal factorization of matrix and operator functions, OT 1, Birkhäuser Verlag (Basel), 1979.

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  • [GKLR] Gohberg, I., Kaashoek, M. A., Lerer, L., Rodman, L.: Minimal divisors of rational matrix functions with prescribed zero and pole structure, in: Topics in Operator Theory, Systems and Networks (Eds. H. Dym and I. Gohberg), OT 12, Birkhäuser Verlag (Basel) 1984, pp 241–275.

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  • [GLR] Gohberg, I, Lancastar, P., Rodman, L.: Matrix polynomials, Academic Press (New York), 1982.

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  • [W] Wonham, M. W.: Linear multivariable control: a geometric approach, Springer-Verlag (New York) 1979.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Israel

    I. Gohberg

  2. Department of Mathematics and Computer Science, Vrije Universiteit, Amsterdam, The Netherlands

    M. A. Kaashoek

Authors
  1. I. Gohberg
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  2. M. A. Kaashoek
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Gohberg, I., Kaashoek, M.A. An inverse spectral problem for rational matrix functions and minimal divisibility. Integr equ oper theory 10, 437–465 (1987). https://doi.org/10.1007/BF01195037

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