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An Interpolation Problem for Functions with Values in a Commutative Ring

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A Panorama of Modern Operator Theory and Related Topics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 218))

Abstract

It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we study an interpolation problem in this setting. A key tool is the principle of permanence of algebraic identities.

Mathematics Subject Classification (2000). 60H40, 93C05.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Ben Gurion University of the Negev, 653, Be’er Sheva, 84105, Israel

    Daniel Alpay

  2. Department of Mathematics, Sami Shamoon College of Engineering, Be’er Sheva, 84100, Israel

    Haim Attia

Authors
  1. Daniel Alpay
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  2. Haim Attia
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Corresponding author

Correspondence to Daniel Alpay .

Editor information

Editors and Affiliations

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

    Harry Dym

  2. Dept. Mathematics &, Computer Sciences, Free University Amsterdam, De Boelelaan 1081 A, Amsterdam, 1081 HV, Netherlands

    Marinus A. Kaashoek

  3. Dept. Mathematics & Statistics, University of Calgary, University Drive NW 2500, Calgary, T2N 1N4, Alberta, Canada

    Peter Lancaster

  4. Inst. Analysis und Scientific Computing, TU Wien, Wiedner Hauptstr. 8-10, Wien, 1040, Austria

    Heinz Langer

  5. Dept. Mathematics, Technion Israel Institute of Technology, Haifa, 32000, Israel

    Leonid Lerer

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Alpay, D., Attia, H. (2012). An Interpolation Problem for Functions with Values in a Commutative Ring. In: Dym, H., Kaashoek, M., Lancaster, P., Langer, H., Lerer, L. (eds) A Panorama of Modern Operator Theory and Related Topics. Operator Theory: Advances and Applications(), vol 218. Springer, Basel. https://doi.org/10.1007/978-3-0348-0221-5_1

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