Wiener-Hopf Integral Operators with Rational Symbols

  • Israel Gohberg
  • Seymour Goldberg
  • Marinus A. Kaashoek
Part of the Operator Theory: Advances and Applications book series (OT, volume 49)


In this chapter we study in more detail Wiener-Hopf integral operators with a rational matrix symbol. The technique of Wiener-Hopf factorization is introduced. The fact that the symbols are rational allows us to represent them in a special way. We use this representation to construct explicitly the factors in a canonical Wiener-Hopf factorization. In this way explicit formulas for the inverse and the Fredholm characteristics are obtained. Also convolution operators on a finite interval are analyzed in terms of the special representation of the symbol. An example from linear transport theory illustrates the general theory.


Matrix Function Half Plane Generalize Inverse Convolution Operator Real Eigenvalue 
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Copyright information

© Springer Basel AG 1990

Authors and Affiliations

  • Israel Gohberg
    • 1
  • Seymour Goldberg
    • 2
  • Marinus A. Kaashoek
    • 3
  1. 1.School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact SciencesTel-Aviv UniversityTel-AvivIsrael
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA
  3. 3.Faculteit Wiskunde en InformaticaVrije UniversiteitAmsterdamThe Netherlands

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