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 
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/
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     title = {Wiener{\textendash}Hopf equations in a~quadrant of the plane, discrete groups, and automorphic functions},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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[3] V. A. Malyshev, “O reshenii diskretnykh uravnenii Vinera–Khopfa v chetverti ploskosti”, DAN SSSR, 187:6 (1969), 1243–1246 | Zbl

[4] N. Wiener, E. Hopf, “Ueber Eine Klasse Singularen Integralgleichungen”, Sitzungsb. Preus. Akad. Wiss., 1931, 696–706 | Zbl

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[6] I. Ts. Gokhberg, L. S. Goldenshtein, “O mnogomernom integralnom uravnenii na poluprostranstve s yadrom, zavisyaschim ot raznosti argumentov, i ego diskretnom analoge”, DAN SSSR, 131:1 (1960), 9–12 | Zbl

[7] I. M. Gelfand, D. A. Raikov, G. E. Shilov, Kommutativnye normirovannye koltsa, Fizmatgiz, Moskva, 1960 | Zbl

[8] E. I. Zverovich, G. S. Litvinchuk, “Kraevye zadachi so sdvigom dlya analiticheskikh funktsii i singulyarnye funktsionalnye uravneniya”, Uspekhi matem. nauk, XXIII:3(141) (1968), 67–121

[9] J. Lehner, Discontinuous groups and automorphic functions, Math. Surveys, VIII, American Math. Soc., Providence, R.I., 1964 | MR

[10] Dzh. Springer, Vvedenie v teoriyu rimanovykh poverkhnostei, IL, Moskva, 1960

[11] L. R. Ford, Avtomorfnye funktsii, ONTI, Moskva–Leningrad, 1936

[12] K. Weierstrass, Vorlesungen uber die theorie der Abelschen transzendenten, Math. Werke, 4, Berlin, 1902 | Zbl

[13] A. Selberg, “On discontinuous groups in higher dimensional symmetric spaces”, Tata Inst. of Fundam. Research, 1960, 147–164 | MR | Zbl

[14] V. A. Malyshev, “Analiticheskii metod v teorii sluchainykh bluzhdanii v chetverti ploskosti: prostoe bluzhdanie s kosym otrazheniem”, Trudy Sovetsko-Yaponskogo simpoziuma po teorii veroyatnostei, Khabarovsk, 1969, 176–184

[15] V. S. Rabinovich, “Mnogomernoe uravnenie Vinera–Khopfa dlya konusov”, Teoriya funktsii, funkts. analiz i ikh prilozheniya, 5 (1957), 59–67

[16] V. A. Kakichev, “Kraevye zadachi lineinogo sopryazheniya dlya funktsii, golomorfnykh v bitsilindricheskikh oblastyakh”, Teoriya funktsii, funkts. analiz i ikh prilozheniya, 1967, no. 5, 37–58 | Zbl