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Topics in Interpolation Theory of Rational Matrix-valued Functions pp 109–122Cite as

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Regular Rational Matrix Functions with Prescribed Pole and Zero Structure

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 33))

Abstract

The problem to construct all regular rational matrix functions with a prescribed pole and zero structure is solved explicitly. Also the necessary and sufficient condition for the existence of a solution is derived. The proofs use an appropriate Möbius transformation to reduce the problem to the case when the functions are regular at infinity.

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References

  1. Ball, J.A., Cohen, N., Ran, A.C.M.: Inverse spectral problems for regular improper rational matrix functions, this volume.

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  2. Ball, J.A., Ran, A.C.M.: Global inverse spectral problems for rational matrix functions, Linear Algebra and Applications 86 (1987), 237–282.

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  3. Ball, J.A., Ran, A.C.M.: Local inverse spectral problems for rational matrix functions, Integral Equations and Operator Theory 10 (1987), 349–415.

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  4. Bart, H., Gohberg, I., Kaashoek, M.A.: Minimal factorization of matrix and operator functions, OT 1, Birkhäuser Verlag, Basel, 1979.

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  5. Gohberg, I., Kaashoek, M.A.: An inverse spectral problem for rational matrix functions and minimal divisibility, Integral Equations and Operator Theory 10 (1987), 437–465.

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  6. 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), OT12, Birkhäuser Verlag, Basel, 1984, pp. 241–275.

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Author information

Authors and Affiliations

  1. Raymond and Beverly Sackler, Faculty of Exact Sciences, 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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Editor information

Editors and Affiliations

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

    I. Gohberg

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© 1988 Springer Basel AG

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Gohberg, I., Kaashoek, M.A. (1988). Regular Rational Matrix Functions with Prescribed Pole and Zero Structure. In: Gohberg, I. (eds) Topics in Interpolation Theory of Rational Matrix-valued Functions. Operator Theory: Advances and Applications, vol 33. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5469-6_3

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  • DOI: https://doi.org/10.1007/978-3-0348-5469-6_3

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5471-9

  • Online ISBN: 978-3-0348-5469-6

  • eBook Packages: Springer Book Archive

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