Wiener–Hopf equations in a quadrant of the plane, discrete groups, and automorphic functions

Operators $A(l_1(Z_2^{++})\to l_1(Z_2^{++}))$ of the form $(A\xi)(x)=\sum_{K\in Z_2^{++}}a(x-k)\xi(k)$, where $a\in l_1(Z_2)$ and $Z_2$ ($Z_2^{++}$) is the set of planar points with integral (nonnegative) coordinates, are considered. Basic results of the paper: invertibility of the operator $A$ is proved, and an analysis is made of analytic properties of the symbol $F\xi$ of the solution of the equation $A\xi=\eta$.
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