The diffraction by a resistive sheet attached to a two-sided impedance
plane, made up by perfectly electric conducting and impedance half-pl
anes, is presented. An E-plane wave normally illuminates this structur
e, therefore, the problem is a two dimensional one. By using Sommerfel
d-Maliuzhinets' method, the problem is reduced to the solution of a co
upled system of functional equations for two spectral functions corres
ponding to the two spatial regions defined by the resistive sheet. By
eliminating either of the spectral functions, a second-order differenc
e equation with variable 2 pi-periodic coefficients is obtained for th
e remaining one. A general method of constructing a single-valued solu
tion of this second-order difference equation is presented based on th
e Fourier transform. It is shown that the obtained single-valued merom
orphic spectral function satisfies the edge condition, pole requiremen
t and the radiation condition.