Local description of entire functions. Submodules of rank 1
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 2, pp. 14-28 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Submodule in the module of entire functions is called ample, if this submodule coincides with its local hull. Ampleness splits in three separate properties: intensity, stability and saturation. In the article submodules of entire functions are investigated for the presence of these properties. Particular attention is paid to submodules of rank 1.
@article{VMJ_2014_16_2_a1,
     author = {T. A. Volkovaya and A. B. Shishkin},
     title = {Local description of entire functions. {Submodules} of rank~1},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {14--28},
     year = {2014},
     volume = {16},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2014_16_2_a1/}
}
TY  - JOUR
AU  - T. A. Volkovaya
AU  - A. B. Shishkin
TI  - Local description of entire functions. Submodules of rank 1
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2014
SP  - 14
EP  - 28
VL  - 16
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMJ_2014_16_2_a1/
LA  - ru
ID  - VMJ_2014_16_2_a1
ER  - 
%0 Journal Article
%A T. A. Volkovaya
%A A. B. Shishkin
%T Local description of entire functions. Submodules of rank 1
%J Vladikavkazskij matematičeskij žurnal
%D 2014
%P 14-28
%V 16
%N 2
%U http://geodesic.mathdoc.fr/item/VMJ_2014_16_2_a1/
%G ru
%F VMJ_2014_16_2_a1
T. A. Volkovaya; A. B. Shishkin. Local description of entire functions. Submodules of rank 1. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 2, pp. 14-28. http://geodesic.mathdoc.fr/item/VMJ_2014_16_2_a1/

[1] Krasichkov-Ternovskii I. F., “Lokalnoe opisanie zamknutykh idealov i podmodulei analiticheskikh funktsii odnoi peremennoi. I”, Izv. AN SSSR. Ser. mat., 43:1 (1979), 44–66 | MR | Zbl

[2] Krasichkov-Ternovskii I. F., “Lokalnoe opisanie zamknutykh idealov i podmodulei analiticheskikh funktsii odnoi peremennoi. II”, Izv. AN SSSR. Ser. mat., 43:2 (1979), 309–341 | MR | Zbl

[3] Krasichkov-Ternovskii I. F., “Abstraktnye priemy lokalnogo opisaniya zamknutykh podmodulei analiticheskikh funktsii”, Mat. sb., 181:12 (1990), 1640–1658 | MR | Zbl

[4] Shishkin A. B., “Lokalnoe opisanie zamknutykh podmodulei v spetsialnom module tselykh funktsii eksponentsialnogo tipa”, Mat. zametki, 46:6 (1989), 94–100 | MR | Zbl

[5] Shishkin A. B., “Spektralnyi sintez dlya operatora, porozhdaemogo umnozheniem na stepen nezavisimoi peremennoi”, Mat. sb., 182:6 (1991), 828–848 | MR | Zbl

[6] Krasichkov-Ternovskii I. F., “Spektralnyi sintez v kompleksnoi oblasti dlya differentsialnogo operatora s postoyannymi koeffitsientami. I. Teorema dvoistvennosti”, Mat. sb., 182:11 (1991), 1559–1587 | MR | Zbl

[7] Shishkin A. B., “Spektralnyi sintez dlya sistem differentsialnykh operatorov s postoyannymi koeffitsientami. Teorema dvoistvennosti”, Mat. sb., 189:9 (1998), 143–160 | DOI | MR | Zbl

[8] Chernyshev A. N., Spektralnyi sintez dlya differentsialnogo operatora beskonechnogo poryadka s postoyannymi koeffitsientami, Dis. $\dots$ kand. fiz.-mat. nauk, Armavir, 2004, 100 pp.

[9] Pismennyi R. G., Glavnye podmoduli i invariantnye podprostranstva analiticheskikh funktsii, Dis. $\dots$ kand. fiz.-mat. nauk, Slavyansk-na-Kubani, 2010, 104 pp.

[10] Volkovaya T. A., Shishkin A. B., “Lokalnoe opisanie tselykh funktsii”, Issledovaniya po mat. analizu, Itogi nauki. Yug Rossii. Mat. forum, 8, ch. 1, YuMI VNTs RAN i RSO-A, Vladikavkaz, 2014, 212–223

[11] Shishkin A. B., “Proektivnoe i in'ektivnoe opisaniya v kompleksnoi oblasti. Dvoistvennost”, Izv. Sarat. un-ta. Novaya ser. Ser. Matematika. Mekhanika. Informatika, 14:1 (2014), 47–65