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A New Proof of an Ellis-Gohberg Theorem on Orthogonal Matrix Functions Related to the Nehari Problem

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Recent Advances in Operator Theory and its Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 160))

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Abstract

The state space method for rational matrix functions and a classical inertia theorem are used to give a new proof of the main step in a recent theorem of R.L. Ellis and I. Gohberg on orthogonal matrix functions related to the Nehari problem. Also we comment on a connection with the Nehari-Takagi interpolation problem.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, North-West University, Private Bag X6001, Potchefstroom, 2520, South Africa

    G.J. Groenewald

  2. Afdeling Wiskunde, Faculteit der Exacte Wetenschappen, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    M.A. Kaashoek

Authors
  1. G.J. Groenewald
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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

    Israel Gohberg

  2. Beer-Sheva

    D. Alpay  & P. A. Fuhrmann  & 

  3. Haifa

    J. Arazy  & L. E. Lerer  & 

  4. Tel Aviv

    A. Atzmon  & A. Ben-Artzi  & 

  5. Blacksburg

    J. A. Ball

  6. Bloomington

    H. Bercovici

  7. Chemnitz

    A. Böttcher  & G. Heinig  & 

  8. Athens, USA

    K. Clancey

  9. Buffalo

    L. A. Coburn

  10. Waterloo, Ontario

    K. R. Davidson

  11. College Station

    R. G. Douglas

  12. Groningen

    A. Dijksma

  13. Rehovot

    H. Dym

  14. Mainz

    B. Gramsch

  15. La Jolla

    J. A. Helton

  16. Amsterdam

    M. A. Kaashoek

  17. Argonne

    H. G. Kaper

  18. Tokyo

    S. T. Kuroda

  19. Calgary

    P. Lancaster

  20. Columbus

    B. Mityagin

  21. Manhattan, Kansas

    V. V. Peller

  22. Williamsburg

    L. Rodman  & I. M. Spitkovsky  & 

  23. Charlottesville

    J. Rovnyak

  24. Berkeley

    D. E. Sarason  & D. Voiculescu  & 

  25. Providence

    S. Treil

  26. Marburg

    H. Upmeier

  27. Leiden

    S. M. Verduyn Lunel

  28. Santa Cruz

    H. Widom

  29. Nashville

    D. Xia

  30. Rennes

    D. Yafaev

  31. Department of Mathematics, FEW Vrije Universiteit, De Boelelaan 1081A, 1081 HV, Amsterdam, The Netherlands

    Marinus A. Kaashoek

  32. Dipartimento di Matematica, UniversitĂ  di Cagliari, Viale Merello 92, 09123, Cagliari, Italy

    Sebastiano Seatzu  & Cornelis van der Mee  & 

Additional information

To Israel Gohberg on the occasion of his 75th birthday, with gratitude and admiration.

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Groenewald, G., Kaashoek, M. (2005). A New Proof of an Ellis-Gohberg Theorem on Orthogonal Matrix Functions Related to the Nehari Problem. In: Gohberg, I., et al. Recent Advances in Operator Theory and its Applications. Operator Theory: Advances and Applications, vol 160. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7398-9_10

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