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Periodic wave-guides revisited: Radiation conditions, limiting absorption principles, and the space of bounded solutions
  • Andreas Kirsch,
  • Ben Schweizer
Andreas Kirsch
Karlsruher Institut fur Technologie Fakultat fur Mathematik

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Ben Schweizer
Technische Universitat Dortmund Fakultat fur Mathematik
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Abstract

We study the Helmholtz equation with periodic coefficients in a closed wave-guide. A functional analytic approach is used to formulate and to solve the radiation problem in a self-contained exposition. In this context, we simplify the non-degeneracy assumption on the frequency. Limiting absorption principles (LAPs) are studied and the radiation condition corresponding to the chosen LAP is derived; we include an example to show different LAPs lead, in general, to different solutions of the radiation problem. Finally, we characterize the set of all bounded solutions to the homogeneous problem.