Inversion of perturbed linear operators that are singular at the origin

نویسندگان

  • Phil Howlett
  • Vladimir Ejov
  • Konstantin Avrachenkov
چکیده

Abstract— We consider the inversion of perturbed linear operators on Hilbert space. Namely, we study linear operators that depend on a small parameter and are singular when the parameter is equal to zero. First we consider the af£ne dependence on the parameter. We treat subsequently the cases of bounded operators with closed range, bounded operators with non closed range, and densely de£ned and closed unbounded operators. Then, we extend the results to the cases of polynomial and analytic perturbations.

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تاریخ انتشار 2008