|Title:||Periodic wave-guides revisited: Radiation conditions, limiting absorption principles, and the space of boundes solutions|
|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.|
|Appears in Collections:||Preprints der Fakultät für Mathematik|
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