Geodesic
On some questions connected with the problem of existence of automorphic analytic functions with given modulus of boundary values
Sbornik. Mathematics, Tome 39 (1981) no. 4, pp. 501-518 
M. V. Samokhin. On some questions connected with the problem of existence of automorphic analytic functions with given modulus of boundary values. Sbornik. Mathematics, Tome 39 (1981) no. 4, pp. 501-518. http://geodesic.mathdoc.fr/item/SM_1981_39_4_a4/
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     title = {On some questions connected with the problem of existence of automorphic analytic functions with given modulus of boundary values},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For an arbitrary region $D$ in the extended plane it is shown that the possibility of constructing automorphic analytic functions with given modulus of boundary values on the universal covering surface of $D$ is a local property of the boundary of $D$ and is equivalent to the possibility of giving a good description of the extremals for a rather large class of problems in this region. Bibliography: 12 titles.

[1] M. V. Samokhin, “Ob avtomorfnykh analiticheskikh funktsiyakh s zadannym modulem granichnykh znachenii”, Matem. sb., 101(143) (1976), 189–203 | Zbl

[2] G. Ts. Tumarkin, S. Ya. Khavinson, “Kachestvennye svoistva reshenii ekstremalnykh zadach nekotorykh tipov”, Issledovaniya po sovremennym problemam teorii funktsii kompleksnogo peremennogo, Fizmatgiz, Moskva, 1960

[3] S. Ya. Khavinson, “Ob analiticheskoi emkosti mnozhestv, sovmestnoi netrivialnosti razlichnykh klassov analiticheskikh funktsii i lemme Shvartsa v proizvolnykh oblastyakh”, Matem. sb., 54(96) (1961), 3–50

[4] D. Hejhal, “Linear extremal problems for analytic functions”, Acta Math., 128 (1972), 91–122 | DOI | MR | Zbl

[5] T. Gamelin, “Extremal problems in arbitrary domains. II”, Michigan Math. J., 21 (1974), 297–307 | MR | Zbl

[6] M. V. Samokhin, “Ob ekstremalnykh zadachakh dlya mnogoznachnykh analiticheskikh funktsii s odnoznachnym modulem”, Sb. trudov MISI im. V. V. Kuibysheva, No 130, 1975

[7] N. S. Landkof, Osnovy sovremennoi teorii potentsiala, izd-vo “Nauka”, Moskva, 1966 | MR

[8] W. Rudin, “Some theorems on bounded analityc functions”, Trans. Amer. Math. Soc., 78 (1955), 333–342 | DOI | MR | Zbl

[9] T. Gamelin, “Localisation of corona problem”, Pacific J. Math., 34 (1970), 73–81 | MR | Zbl

[10] T. Gamelin, “Extremal problems in arbitrary domains”, Michigan Math. J., 20 (1973), 3–11 | DOI | MR | Zbl

[11] M. Tsuji, Potential theory in modern function theory, Maruzen, Tokyo, 1959 | MR | Zbl

[12] S. Ya. Khavinson, “O probleme Karateodori–Feiera dlya analiticheskikh funktsii v konechno-svyaznykh oblastyakh”, Uchenye zapiski Vladimirskogo gos. ped. in-ta fiz.-matem. seriya, vyp. II, 1955