Geodesic
The divisor of a generalized analytic function
Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 655-661 
S. A. Grigoryan. The divisor of a generalized analytic function. Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 655-661. http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a1/
@article{MZM_1997_61_5_a1,
     author = {S. A. Grigoryan},
     title = {The divisor of a~generalized analytic function},
     journal = {Matemati\v{c}eskie zametki},
     pages = {655--661},
     year = {1997},
     volume = {61},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a1/}
}
TY  - JOUR
AU  - S. A. Grigoryan
TI  - The divisor of a generalized analytic function
JO  - Matematičeskie zametki
PY  - 1997
SP  - 655
EP  - 661
VL  - 61
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a1/
LA  - ru
ID  - MZM_1997_61_5_a1
ER  - 
%0 Journal Article
%A S. A. Grigoryan
%T The divisor of a generalized analytic function
%J Matematičeskie zametki
%D 1997
%P 655-661
%V 61
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a1/
%G ru
%F MZM_1997_61_5_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

For generalized analytic functions, we define the order of a zero and prove the following division theorem: if the orders of zeros of the numerator majorize those of the denominator, then the fraction is a generalized analytic function.

[1] Grigoryan S. A., “Obobschennye analiticheskie funktsii”, UMN, 49:2 (1994), 3–43 | MR

[2] Grigoryan S. A., “Maksimalnye algebry obobschennykh analiticheskikh funktsii”, Izv. AN ArmSSR, 15:5 (1981), 358–365 | MR

[3] Grigoryan S. A., “Obobschennye meromorfnye funktsii”, Izv. RAN. Ser. matem., 57:1 (1993), 147–166 | MR | Zbl

[4] Arens R., Singer I., “Generalized analytic functions”, Trans. Amer. Math. Soc., 81 (1956), 379–393 | DOI | MR | Zbl

[5] Levitan B. M., Pochti periodicheskie funktsii, GITTL, M., 1953

[6] Jessen B., “Über die Nullstellen einer analytischen fastperodischen Function”, Math. Ann., 108 (1933), 485–516 | DOI | MR | Zbl

[7] Arens R., “The boundary integral of $\log|\Phi|$ for generalized analytic functions”, Trans. Amer. Math. Soc., 86 (1957), 57–69 | DOI | MR | Zbl

[8] Gofman K., Banakhovy prostranstva analiticheskikh funktsii, IL, M., 1975

[9] Bor G., Pochti periodicheskie funktsii, OGIZ, M., 1934

[10] Gamelin T., Ravnomernye algebry, Mir, M., 1973 | Zbl