The Calculus of Parameter-Dependent Operators

  • Gerd Grubb
Part of the Progress in Mathematics book series (PM, volume 65)


The next two chapters contain the full machinery of the parameter-dependent calculus, which is developed ir. order to give a convenient framework for the study of resolvents and evolution problems and other problems with an unbounded parameter. To demonstrate the usefulness of the systematic point of view, we have inserted Examples 2.1.23 and 2.2.14, where some “hand” calculations in connectior. with the simple pseudodifferential operator
$$ P + {\mu ^2} = \frac{{D_{{x_1}}^4 + D_{{x_2}}^4}}{{D_{{x_1}}^2 + D_{{x_2}}^2}} + {\mu ^2} $$
are attempted.


Transmission Condition Trace Operator Principal Symbol Symbol Space Symbol Class 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Gerd Grubb
    • 1
  1. 1.Københavns Universitets Matematiske InstitutKøbenhavn ØDenmark

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