On matrix equations appearing when solving wave scattering problems for planar waveguide structures with rectangular region of interaction

Matrix-operator equations that occur when applying the domain-product technique (DPT) to problems of scattering in planar waveguide transformers with a rectangular connecting region are studied. It is shown that the technique results in the systems solvable in the space l̃
₂
by means of the truncation method convergent in the norm.