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Inversion of perturbed linear operators that are singular at the origin Phil Howlett, Vladimir Ejov,
 

Summary: Inversion of perturbed linear operators that are singular at the origin
Phil Howlett, Vladimir Ejov,
CIAM, University of South Australia
Mawson Lakes 5095, Australia
emails: p.howlett@unisa.edu.au,
vladimir.ejov@unisa.edu.au
Konstantin Avrachenkov,
INRIA Sophia Antipolis,
2004, Route des Lucioles, B.P.93,
Sophia Antipolis Cedex, 06902, France
email: k.avrachenkov@sophia.inria.fr
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 afŁne depen­
dence on the parameter. We treat subsequently the cases of
bounded operators with closed range, bounded operators with
non closed range, and densely deŁned and closed unbounded
operators. Then, we extend the results to the cases of polynomial
and analytic perturbations.

  

Source: Avrachenkov, Konstantin - INRIA Sophia Antipolis

 

Collections: Computer Technologies and Information Sciences