Geodesic
Wiener--Hopf equations in a~quadrant of the plane, discrete groups, and automorphic functions
Sbornik. Mathematics, Tome 13 (1971) no. 4, pp. 491-516

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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 $A\xi=\eta$. Figures: 4. Bibliography: 16 titles. 
@article{SM_1971_13_4_a0,
     author = {V. A. Malyshev},
     title = {Wiener--Hopf equations in a~quadrant of the plane, discrete groups, and automorphic functions},
     journal = {Sbornik. Mathematics},
     pages = {491--516},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_13_4_a0/}
}
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V. A. Malyshev. Wiener--Hopf equations in a~quadrant of the plane, discrete groups, and automorphic functions. Sbornik. Mathematics, Tome 13 (1971) no. 4, pp. 491-516. http://geodesic.mathdoc.fr/item/SM_1971_13_4_a0/