Zeros of holomorphic functions of finite order and weighted estimates for solutions of the $\bar\partial$-equation
Sbornik. Mathematics, Tome 35 (1979) no. 4, pp. 449-459 Cet article a éte moissonné depuis la source Math-Net.Ru

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A characterization is given for the zero-sets of functions holomorphic in a strictly pseudoconvex manifold and having finite order of growth at the boundary of the manifold. The characterization is obtained by means of explicit formulas for solutions of the equation $\bar\partial u=f$ on a strictly convex domain in $\mathbf C^n$, valid for right sides $f$ having finite order of growth at the boundary of the domain. Bibliography: 16 titles.
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     title = {Zeros of holomorphic functions of finite order and weighted estimates for solutions of the $\bar\partial$-equation},
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Sh. A. Dautov; G. M. Henkin. Zeros of holomorphic functions of finite order and weighted estimates for solutions of the $\bar\partial$-equation. Sbornik. Mathematics, Tome 35 (1979) no. 4, pp. 449-459. http://geodesic.mathdoc.fr/item/SM_1979_35_4_a0/

[1] L. A. Aizenberg, Sh. A. Dautov, Differentsialnye formy, ortogonalnye golomorfnym funktsiyam ili formam, i ikh svoistva, izd-vo “Nauka”, Novosibirsk, 1975 | MR

[2] F. Griffits, Dzh. King, Teoriya Nevanlinny i golomorfnye otobrazheniya algebraicheskikh mnogoobrazii, izd-vo “Mir”, Moskva, 1976 | MR

[3] M. M. Dzhrbashyan, “K probleme predstavimosti analiticheskikh funktsii”, Soobsch. in-ta matem. i mekh. AN Arm. SSR, 1948, no. 2, 3–40

[4] R. Nevanlinna, Odnoznachnye analiticheskie funktsii, Gostekhizdat, Moskva–Leningrad, 1941 | MR

[5] A. V. Romanov, G. M. Khenkin, “Tochnye gelderovskie otsenki reshenii $\bar\partial$-uravneniya”, Izv. AN SSSR, seriya matem., 35 (1971), 1171–1183 | MR | Zbl

[6] G. M. Khenkin, “Resheniya s otsenkami uravnenii G. Levi i Puankare–Lelona. Postroenie funktsii klassa Nevanlinny s zadannymi nulyami v strogo predvypukloi oblasti”, DAN SSSR, 224:4 (1975), 771–774 | MR | Zbl

[7] G. M. Khenkin, “Uravnenie G. Levi i analiz na psevdovypuklom mnogoobrazii”, Uspekhi matem. nauk, XXXII:3(195) (1977), 57–118

[8] G. M. Khenkin, “Uravnenie G. Levi i analiz na psevdovypuklom mnogoobrazii. II”, Matem. sb., 102(144) (1977), 71–108 | Zbl

[9] R. O. Kujala, “Generalized Blaschke conditions on the unit ball in $\mathbf C^n$”, Value-distribution theory, part A, Marcel Oekker, New York, 1974, 249–261 | MR

[10] P. Lelong, Fonctions plurisous-harmoniques et formes differentielles positive, Gordon Breach, Paris, 1968 | MR | Zbl

[11] G. Mueller, Functions of finite order on the ball, Dissertation, Univ. of Notre Dame, 1971 | Zbl

[12] H. Sckoda, “Sous-ensemles analytiques d'odre fini on infini dans $\mathbf C^n$”, Bull. Soc. Math. France, 100 (1972), 403–408

[13] H. Sckoda, “Zéros des fonctions de la classe Nevanlinna dans les ouverts strictement pseudoconvexes”, C. r Acad, scient. Paris, 280:A (1975), 633–636 | MR

[14] H. Sckoda, “Valeurs au bord pour les solutions de l'operateur d"et caracterisation des zeros des fonctions de la classe de Nevanlinna”, Bull. Soc. Math. France, 104 (1976), 225–299 | MR

[15] W. Stoll, “Holomorphic functions of finite order in several complex variables”, Conf. board of the math, science regional conference series in math., 21, Amer. Math. Soc, Providence, 1974 | MR | Zbl

[16] N. Weyland, “Fonctions holomorpfes d'odre fini dans les domaines strictement convexes”, C. r. Acad. scient. Paris, 283:A (1976), 697–699 | MR | Zbl