Some applications of functional analysis in classical scattering

  • R. E. Kleinman
Classical Scattering Theory
Part of the Lecture Notes in Physics book series (LNP, volume 130)


Problems in classical scattering, the Dirichlet, Neumann, and transmission problems for the Helmholtz equation, and the problem of a perfect reflector for Maxwell's equations are formulated as problems in integral equations. The spectrum of the integral operators is shown to vary in each case. However, a result from func tional analysis on the perturbation of spectra is used not only to establish existence and uniqueness, but also to provide an iterative method for actually constructing the solution in each example.


Integral Equation Spectral Radius Neumann Problem Boundary Integral Equation Helmholtz Equation 
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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • R. E. Kleinman
    • 1
  1. 1.Department of Mathematical SciencesUniversity of DelawareNewark

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