Geodesic
Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis
Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 3-17 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the work we consider a topological module $\mathcal P$ of entire functions, which is the isomorphic image under the Fourier–Laplace transform of Schwarz space $\mathcal E'$ of distributions compactly supported in a finite or infinite interval $(a;b)\subset\mathbb R$. We study some properties of closed submodules in module $\mathcal P$ related with local description problem. We also study issues on duality between closed submodules in $\mathcal P$ and subspaces in the space $\mathcal E=C^\infty(a;b)$ invariant w.r.t. the differentiation.
Keywords: entire functions, local description of submodules, invariant subspaces, spectral synthesis, finitely generated submodules.
Mots-clés : Fourier–Laplace transform 
@article{UFA_2014_6_4_a0,
     author = {N. F. Abuzyarova},
     title = {Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis},
     journal = {Ufa mathematical journal},
     pages = {3--17},
     year = {2014},
     volume = {6},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a0/}
}
TY  - JOUR
AU  - N. F. Abuzyarova
TI  - Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis
JO  - Ufa mathematical journal
PY  - 2014
SP  - 3
EP  - 17
VL  - 6
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a0/
LA  - en
ID  - UFA_2014_6_4_a0
ER  - 
%0 Journal Article
%A N. F. Abuzyarova
%T Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis
%J Ufa mathematical journal
%D 2014
%P 3-17
%V 6
%N 4
%U http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a0/
%G en
%F UFA_2014_6_4_a0
N. F. Abuzyarova. Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis. Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 3-17. http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a0/

[1] Sebastyan-i-Silva Zh., “O nekotorykh klassakh LVP, vazhnykh v prilozheniyakh”, Matematika. Sb. perevodov instrannykh statei, 1:1 (1957), 60–77

[2] Levin B. Y., Lectures on entire functions, Rev. Edition, AMS, Providence, Rhode Island, 1996, 254 pp., (in collaboration with Yu. Lyubarskii, M. Sodin, V. Tkachenko) | MR | Zbl

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

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

[5] Krasichkov-Ternovskii I. F., “Invariantnye podprostranstva analiticheskikh funktsii. I. Spektralnyi sintez na vypuklykh oblastyakh”, Matem. sbornik, 87(129):4 (1972), 459–489 | MR | Zbl

[6] Abuzyarova N. F., “Ob odnom svoistve podprostranstv, dopuskayuschikh spektralnyi sintez”, Matem. sbornik, 190:4 (1999), 3–22 | DOI | MR | Zbl

[7] Abuzyarova N. F., “Konechno porozhdennye podmoduli v module tselykh funktsii, opredelyaemom ogranicheniyami na indikator”, Matem. zametki, 71:1 (2002), 3–17 | DOI | MR | Zbl

[8] Khabibullin B. N., “Spektralnyi sintez dlya peresecheniya invariantnykh podprostranstv golomorfnykh funktsii”, Matem. sbornik, 196:3 (2005), 119–142 | DOI | MR | Zbl

[9] Khabibullin B. N., “Zamknutye podmoduli golomorfnykh funktsii, porozhdennye podmodulyami, dopuskayuschimi lokalnoe opisanie”, Geometricheskaya teoriya funktsii i kraevye zadachi, Trudy matem. tsentra im. N. I. Lobachevskogo, 14, 2002, 280–298 | MR | Zbl

[10] Khabibullin B. N., “Zamknutye podmoduli golomorfnykh funktsii s dvumya porozhdayuschimi”, Funkts. analiz i ego prilozheniya, 38:1 (2004), 65–80 | DOI | MR | Zbl

[11] Khabibullin B. N., “Zamknutye idealy golomorfnykh funktsii s dvumya porozhdayuschimi”, Matem. zametki, 76:4 (2004), 604–609 | DOI | MR | Zbl

[12] Aleman A., Korenblum B., “Derivation-Invariant Subspaces of $C^\infty$”, Computation Methods and Function Theory, 8:2 (2008), 493–512 | DOI | MR | Zbl

[13] Khermander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, v. 1, Teoriya raspredelenii i analiz Fure, Mir, M., 1986, 462 pp.

[14] Sedletskii A. M., “Analiticheskie preobrazovaniya Fure i eksponentsialnye approksimatsii. I”, Sovr. matem. Fund. napravleniya, 5, 2003, 3–152 | MR | Zbl