A spectral method in the theory of wave propagation in cellular periodic waveguides

A spectral method for the analysis of wave propagation in cellular periodic waveguides is demonstrated using as an example the problem of determining normal waves in a corrugated waveguide with rectangular corrugations. A proof is presented for a theorem which is an analog of the Wiener-Paley theorem for Fourier series; the theorem is used to demonstrate the equivalence of the solutions to the initial boundary value problem and to the dispersion equation.