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Abstract

The purpose of this note is to describe an approach to scattering theory, developed by Lax and Phillips, which is especially appropriate for hyperbolic equations. Since the classical steady-state theory of scattering was developed from the point of view of elliptic equations, it is to be expected that our approach will bring new insights into the problem. So far these new insights have resulted more in conjectures than in theorems, never-the-less a beginning has been made and we shall list some of the recent results obtained by P. D. Lax, D. Ludwig, C. S. Morawetz, and Phillips.

Keywords

Hyperbolic Equation Exterior Domain Multiplicative Operator High Frequency Part Pure Point Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    P. D. Lax and R. S. Phillips, Scattering theory. Academic Press, New York 1967.Google Scholar
  2. [2]
    P. D. Lax, C. S. Morawetz and R. S. Phillips, Exponential decay of solutions of the wave equation in the exterior of a star-shaped obstacle. Comm. Pure and Appl. Math. 16 (1963), 477–486.CrossRefGoogle Scholar
  3. [3]
    D. Ludwig and C. S. Morawetz, The generalized Huyghens’ Principle for reflecting bodies. Comm.Pure and Appl. Math., to appear.Google Scholar
  4. [4]
    C. S. Morawetz, The decay of solutions of the exterior initial-boundary value problem for the wave equation. Comm. Pure and Appl. Math. 14 (1961), 561–568.CrossRefGoogle Scholar
  5. [5]
    R. S. Phillips, A remark on the preceding paper of D. Ludwig and C. S. Morawetz. Comm. Pure and Appl. Math., to appear.Google Scholar
  6. [6]
    I. E. Segal and Y. Fourès, Causality and analyticity. Trans. Amer. Math. Soc. 78 (1955), 385–405.Google Scholar

Copyright information

© Springer Basel AG 1969

Authors and Affiliations

  • R. S. Phillips
    • 1
    • 2
  1. 1.Stanford UniversityUSA
  2. 2.Århus UniversityDenmark

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