Optical diffraction on a periodical interface belongs to relatively lowly exploited applications of the boundary integral equations method. This contribution presents a less frequent approach to the diffraction problem based on vector tangential fields of electromagnetic intensities. The problem is formulated as the system of boundary integral equations for tangential fields, for which existence and uniqueness of weak solution is proved. The properties of introduced boundary operators with singular...

Let $M_{m,n}$ be the space of all complex m × n matrices. The generalized unit disc in $M_{m,n}$ is >br>    $R_{m,n}=Z\in M_{m,n}:I^{\left(m\right)}-ZZ*ispositivedefinite$. Here $I^{\left(m\right)}\in M_{m,m}$ is the unit matrix. If 1 ≤ p < ∞ and α > -1, then $L_{\alpha }^p\left(R_{m,n}\right)$ is defined to be the space $L^p{R}_{m,n};{\left[det(I^{\left(m\right)}-ZZ*)\right]}^{\alpha }d{\mu }_{m,n}\left(Z\right)$, where ${\mu }_{m,n}$ is the Lebesgue measure in $M_{m,n}$, and $H_{\alpha }^p\left(R_{m,n}\right)\subset L_{\alpha }^p\left(R_{m,n}\right)$ is the subspace of holomorphic functions. In [8,9] M. M. Djrbashian and A. H. Karapetyan proved that, if $Re\beta >(\alpha +1)/p-1$ (for 1 < p < ∞) and Re β ≥ α (for p = 1), then     $f\left(\right)=T_{m,n}^{\beta }\left(f\right)\left(\right),\in R_{m,n},$where $T_{m,n}^{\beta }$ is the integral operator defined by (0.13)-(0.14). In the present paper, given 1 ≤ p <...