A Class of Ordinary Differential Operators on a Half Line

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


Ordinary differential operators on a half line differ considerably from their counterparts on a finite interval. In this chapter these differences are illustrated for a specific class of differential operators on [0, ∞). The operators involved do not have a compact resolvent. Their spectra and essential spectra are described. Also, the Green’s function and the Fredholm characteristics are computed explicitly. The first four sections concern first order constant coefficient differential operators. Applications to Wiener-Hopf integral equations appear in the fifth section. In the last section the results are extended to higher order differential operators on [0, ∞).


Differential Operator Half Plane Bounded Linear Operator Imaginary Axis Essential Spectrum 
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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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