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Orthogonal Rational Functions


Part of Cambridge Monographs on Applied and Computational Mathematics

  • Date Published: July 2009
  • availability: Available
  • format: Paperback
  • isbn: 9780521115919

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About the Authors
  • This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalised and treated in detail. The same topics are discussed for the different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modelling, lossless inverse scattering, and network synthesis. This theory has many applications in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering.

    • This is the first book of its kind completely devoted to this subject
    • Theory has many applications in real & complex analysis, numerical analysis and electrical engineering
    • Classical problems are generalised and treated in detail
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    Reviews & endorsements

    'The text is written with great clarity … A book with four authors is not common, but these four … are to be applauded for their achievement.' J. H. McCabe

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    Product details

    • Date Published: July 2009
    • format: Paperback
    • isbn: 9780521115919
    • length: 424 pages
    • dimensions: 229 x 152 x 24 mm
    • weight: 0.62kg
    • contains: 18 b/w illus.
    • availability: Available
  • Table of Contents

    List of symbols
    1. Preliminaries
    2. The fundamental spaces
    3. The kernel functions
    4. Recurrence and second kind functions
    5. Para-orthogonality and quadrature
    6. Interpolation
    7. Density of the rational functions
    8. Favard theorems
    9. Convergence
    10. Moment problems
    11. The boundary case
    12. Some applications

  • Resources for

    Orthogonal Rational Functions

    Adhemar Bultheel, Pablo Gonzalez-Vera, Erik Hendriksen, Olav Njastad

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  • Authors

    Adhemar Bultheel, Katholieke Universiteit Leuven, Belgium

    Pablo Gonzalez-Vera, Universidad de la Laguna, Tenerife

    Erik Hendriksen, Universiteit van Amsterdam

    Olav Njastad, Norges Teknisk-Naturvitenskapelige Universitet (Ntnu), Norway

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