Asymptotic perturbation theory

Part of the Classics in Mathematics book series (volume 132)


In the foregoing chapters we have been concerned almost exclusively with analytic or uniform perturbation theory, in which the continuity in norm of the resolvent in the parameter plays the fundamental role. We shall now go into a study in which the basic notion is the strong continuity of the resolvent. Here the assumptions are weakened to such an extent that the analyticity of the resolvent or of the eigenvalues of the operator as functions of the parameter cannot be concluded, but we shall be able to deduce, under suitable conditions, the possibility of asymptotic expansions of these quantities.


Hilbert Space Asymptotic Expansion Continuous Spectrum Strong Convergence Generalize Sense 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  1. 1.University of CaliforniaBerkeleyUSA

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