Geodesic
Zero sets for classes of entire functions and a representation of meromorphic functions
Matematičeskie zametki, Tome 59 (1996) no. 4, pp. 611-617 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $M$ be a continuous real-valued function on $\mathbb C^n$, $n\ge1$, and let $E(M)$ be the class of entire functions $f$ on $\mathbb C^n$ such that $\log|f|\le M$. We give a dual statement for the problem of the description of zero sets of functions in $E(M)$ and the possibility of representing functions $f$ meromorphic on $\mathbb C^n$ by ratios $f=g/h$, where $g$ and $h$ are entire functions belonging to $E(M)$ and coprime at each point $z\in\mathbb C^n$. The dual approach suggested in the paper is new even for the case $n=1$. 
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B. N. Khabibullin. Zero sets for classes of entire functions and a representation of meromorphic functions. Matematičeskie zametki, Tome 59 (1996) no. 4, pp. 611-617. http://geodesic.mathdoc.fr/item/MZM_1996_59_4_a11/

[1] Khabibullin B. N., “Mnozhestva edinstvennosti v prostranstvakh tselykh funktsii odnoi peremennoi”, Izv. AN SSSR. Ser. matem., 55:5 (1991), 1101–1123

[2] Khabibullin B. N., “Naimenshaya plyurisupergarmonicheskaya mazhoranta i multiplikatory tselykh funktsii”, Sib. matem. zh., 33:1 (1992), 173–178 | MR

[3] Khabibullin B. N., “Teorema o naimenshei mazhorante i ee primeneniya. 1: Tselye i meromorfnye funktsii”, Izv. RAN. Ser. matem., 57:1 (1993), 129–146 | Zbl

[4] Akilov G. P., Kutateladze S. S., Uporyadochennye vektornye prostranstva, Nauka, Novosibirsk, 1978 | Zbl

[5] Brelo M., Osnovy klassicheskoi teorii potentsiala, Mir, M., 1964 | Zbl

[6] Khermander L., Vvedenie v teoriyu funktsii neskolkikh kompleksnykh peremennykh, Mir, M., 1968

[7] Goldberg A. A., “O predstavlenii meromorfnoi funktsii v vide chastnogo tselykh funktsii”, Izv. vuzov. Matem., 1972, no. 10, 13–17 | MR | Zbl

[8] Scoda H., “Solution a croisance du second probléme de Cousin dans $\mathbb C^n$”, Ann. Inst. Fourier, 21:1 (1971), 11–23 | MR