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Nevanlinna-Pick Interpolation via Graph Spaces and Kreĭn-space Geometry: A Survey

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Mathematical Methods in Systems, Optimization, and Control

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 222))

Abstract

The Grassmannian/Kreĭn-space approach to interpolation theory introduced in the 1980s gives a Kreĭn-space geometry approach to arriving at the resolvent matrix which parametrizes the set of solutions to a Nevanlinna- Pick interpolation or Nehari-Takagi best-approximation problem. We review the basics of this approach and then discuss recent extensions to multivariable settings which were not anticipated in the 1980s.

Mathematics Subject Classification.47A57

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Authors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061-0123, USA

    Joseph A. Ball

  2. Department of Mathematics & Computer Science, CUNY-BCC, Bronx, NY, 10453, USA

    Quanlei Fang

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  1. Joseph A. Ball
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  2. Quanlei Fang
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Correspondence to Joseph A. Ball .

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Editors and Affiliations

  1. Dept. Mathematics, Weizmann Institute of Science, Rehovot, Israel

    Harry Dym

  2. , Department of Mechanical and, University of California San Diego, Gilman Drive 9500, La Jolla, 92093-0411, California, USA

    Mauricio C. de Oliveira

  3. College of Letters & Science, Dept. Mathematics, University of California, Santa Barbara, Santa Barbara, 93106, California, USA

    Mihai Putinar

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Dedicated to Bill Helton, a dear friend and collaborator

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Ball, J.A., Fang, Q. (2012). Nevanlinna-Pick Interpolation via Graph Spaces and Kreĭn-space Geometry: A Survey. In: Dym, H., de Oliveira, M., Putinar, M. (eds) Mathematical Methods in Systems, Optimization, and Control. Operator Theory: Advances and Applications, vol 222. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0411-0_7

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