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Finite Section Method for Difference Equations

  • I. Gohberg
  • M. A. Kaashoek
  • F. van Schagen
Conference paper
  • 286 Downloads
Part of the Operator Theory: Advances and Applications book series (OT, volume 130)

Abstract

A finite section method is developed for linear difference equations over an infinite time interval. A necessary and sufficient condition is given in order that the solutions of such equations may be obtained as limits of solutions of corresponding equations over a finite time interval. Both the time-variant and the time-invariant case are considered. For the time-invariant case the condition reduces to the requirement that two subspaces defined in terms of the equations should be complementary. The results obtained extend those derived earlier for linear ordinary differential equations.

Keywords

Difference Equation Bounded Sequence Finite Time Interval Spectral Projection Invertible Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • I. Gohberg
    • 1
  • M. A. Kaashoek
    • 2
  • F. van Schagen
    • 2
  1. 1.School of Mathematical SciencesTel Aviv UniversityRamat AvivIsrael
  2. 2.Division of Mathematics and Computer ScienceVrije UniversiteitAmsterdamThe Netherlands

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