Geodesic
On the possibility of holomorphic extension, into a domain, of functions defined on a connected piece of its boundary. II
Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 1-10 Cet article a éte moissonné depuis la source Math-Net.Ru

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This article is a continuation of [1] (see also [2]), in which simple criteria were obtained for the existence of holomorphic extension, into a domain, of a function defined on a connected piece of its boundary. The main result was obtained for the case when the domain is a “truncated” ball. Here we consider a wider class of domains and obtain corresponding criteria in explicit analytic form. For the case of a “truncated” ball these criteria are simpler than the ones in [1]. 
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L. A. Aizenberg; A. M. Kytmanov. On the possibility of holomorphic extension, into a domain, of functions defined on a connected piece of its boundary. II. Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 1-10. http://geodesic.mathdoc.fr/item/SM_1994_78_1_a0/

[1] Aizenberg L. A., Kytmanov A. M., “O vozmozhnosti golomorfnogo prodolzheniya funktsii, zadannykh na svyaznom kuske ee granitsy”, Matem. sb., 182:4 (1991), 490–507

[2] Aizenberg L. A., Kytmanov A. M., O vozmozhnosti golomorfnogo prodolzheniya v oblast funktsii, zadannykh na svyaznom kuske ee granitsy, Preprint No 50M, AN SSSR. Sib. otd. In-t fiziki, Krasnoyarsk, 1990 | MR | Zbl

[3] Chirka E. M., “Analiticheskoe predstavlenie $CR$-funktsii”, Matem. sb., 98(140):4(12) (1975), 591–623 | MR | Zbl

[4] Aizenberg L. A., Dautov Sh. A., Differentsialnye formy, ortogonalnye golomorfnym funktsiyam ili formam, i ikh svoistva, Nauka, Novosibirsk, 1975 | MR

[5] Khërmander L., Vvedenie v teoriyu funktsii neskolkikh peremennykh, Mir, M., 1968

[6] Khenkin G. M., “Integralnoe predstavlenie funktsii, golomorfnykh v strogo psevdovypuklykh oblastyakh i nekotorye prilozheniya”, Matem. sb., 78(112) (1969), 611–632 | MR | Zbl

[7] Ramirez de Arellano E., “Ein Divisionsproblem and Randintegraldarstellungen in der komplexen Analysis”, Math. Ann., 184:3 (1970), 172–187 | DOI | Zbl

[8] Khenkin G. M., “Metod integralnykh predstavlenii v kompleksnom analize”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 7, VINITI, M., 1985, 23–124 | MR

[9] Aizenberg L. A., Mityagin B. S., “Prostranstva funktsii, analiticheskikh v kratno-krugovykh oblastyakh”, Sib. matem. zhurn., 1:2 (1960), 153–170 | MR | Zbl

[10] Rudin U., Teoriya funktsii v edinichnom share iz $\mathbb C^n$, Mir, M., 1984 | MR | Zbl

[11] Aizenberg L. A., “Integralnye predstavleniya funktsii, golomorfnykh v $n$-krugovykh oblastyakh”, Matem. sb., 65(107) (1964), 104–143 | MR | Zbl

[12] Aizenberg L. A., “Rasprostranenie integralnykh predstavlenii s yadrami i kvaziyadrami Segë dlya $n$-krugovykh oblastei”, Nekotorye svoistva golomorfnykh funktsii mnogikh kompleksnykh peremennykh, Sb. nauchn. tr., IFSO AN SSSR, Krasnoyarsk, 1973, 3–34 | MR

[13] Aizenberg L. A., Yuzhakov A. P., Integralnye predstavleniya i vychety v mnogomernom kompleksnom analize, Nauka, Novosibirsk, 1979

[14] Zinovev B. S., “O vosproizvodyaschikh yadrakh dlya kratno-krugovykh oblastei golomorfnosti”, Sib. matem. zhurn., 15:1 (1974), 35–48 | MR | Zbl

[15] Aizenberg L. A., “Simple conditions for holomorphic continuation from part of the boundary of a convex domain to the whole domain”, Trita Mat. Royal Inst. of Techn. Stockholm, 1991, no. 0015, 1–7