Periodic wave-guides revisited: Radiation conditions, limiting
absorption principles, and the space of bounded solutions
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.