Division theorem in some weighted spaces of entire functions
Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 3, pp. 3-20 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider weighted spaces of entire functions which are dual to the Beurling spaces of ultradifferentiable functions of mean type. We prove a division theorem, which completely characterizes all divisors of these spaces. With the help of this theorem, we obtain a criterion for the solvability of convolution equations in the Beurling classes of mean type.
@article{VMJ_2010_12_3_a0,
     author = {A. V. Abanin and D. A. Abanina},
     title = {Division theorem in some weighted spaces of entire functions},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {3--20},
     year = {2010},
     volume = {12},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2010_12_3_a0/}
}
TY  - JOUR
AU  - A. V. Abanin
AU  - D. A. Abanina
TI  - Division theorem in some weighted spaces of entire functions
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2010
SP  - 3
EP  - 20
VL  - 12
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMJ_2010_12_3_a0/
LA  - ru
ID  - VMJ_2010_12_3_a0
ER  - 
%0 Journal Article
%A A. V. Abanin
%A D. A. Abanina
%T Division theorem in some weighted spaces of entire functions
%J Vladikavkazskij matematičeskij žurnal
%D 2010
%P 3-20
%V 12
%N 3
%U http://geodesic.mathdoc.fr/item/VMJ_2010_12_3_a0/
%G ru
%F VMJ_2010_12_3_a0
A. V. Abanin; D. A. Abanina. Division theorem in some weighted spaces of entire functions. Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 3, pp. 3-20. http://geodesic.mathdoc.fr/item/VMJ_2010_12_3_a0/

[1] Ehrenpreis L., “Solution of some problems of division”, Amer. J. Math., 82 (1960), 522–588 | DOI | MR | Zbl

[2] Meise R., Taylor B. A., Vogt D., “Equivalence of slowly decreasing conditions and local Fourier expansions”, Indiana Univ. Math. J., 36:4 (1987), 729–756 | DOI | MR | Zbl

[3] Braun R. W., Meise R., Taylor B. A., “Ultradifferentiable functions and Fourier analysis”, Results Math., 17 (1990), 206–237 | DOI | MR | Zbl

[4] Momm S., “Closed principal ideals in nonradial Hörmander algebras”, Arch. Math., 58 (1992), 47–55 | DOI | MR | Zbl

[5] Korobeinik Yu. F., “O resheniyakh nekotorykh funktsionalnykh uravnenii v klassakh funktsii, analiticheskikh v vypuklykh oblastyakh”, Mat. sb., 75(117):2 (1968), 225–234 | MR | Zbl

[6] Epifanov O. V., “Razreshimost uravneniya svertki v vypuklykh oblastyakh”, Mat. zametki, 15:5 (1974), 787–796 | MR | Zbl

[7] Tkachenko V. A., “Uravneniya tipa svertki v prostranstvakh analiticheskikh funktsionalov”, Izv. AN SSSR. Ser. matem., 41:2 (1977), 378–392 | MR | Zbl

[8] Abanin A. V., Filipev I. A., “Analiticheskaya realizatsiya prostranstv, sopryazhennykh k prostranstvam beskonechno differentsiruemykh funktsii”, Sib. mat. zhurn., 47:3 (2006), 485–500 | MR | Zbl

[9] Abanina D.A., “On Borel's theorem for spaces of ultradifferentiable functions of mean type”, Results Math., 44 (2003), 195–213 | DOI | MR | Zbl

[10] Robertson A. P., Robertson V. Dzh., Topologicheskie vektornye prostranstva, Mir, M., 1967, 257 pp. | MR | Zbl

[11] Abanin A. V., “O multiplikatorakh prostranstva tselykh funktsii, zadavaemogo neradialnym dvuchlennym vesom”, Vladikavk. mat. zhurn., 10:4 (2008), 10–16 | MR

[12] Korobeinik Yu. F., “O multiplikatorakh vesovykh funktsionalnykh prostranstv”, Anal. Math., 15:2 (1989), 105–114 | DOI | MR

[13] Abanin A. V., “O nekotorykh priznakakh slaboi dostatochnosti mnozhestv v induktivnykh predelakh vesomykh prostranstv”, Mat. zametki, 40:4 (1986), 442–454 | MR | Zbl

[14] Abanin A. V., “Gustye prostranstva i analiticheskie multiplikatory”, Izv. vuzov. Sev.-Kavk. region. Estestv. nauki, 1994, no. 4, 3–10 | MR | Zbl

[15] Zharinov V. V., “Kompaktnye semeistva LVP i prostranstva $FS$ i $DFS$”, Uspekhi mat. nauk, 34:4 (1979), 97–131 | MR | Zbl

[16] Sebashtyan-i-Silva Zh., “O nekotorykh klassakh lokalno vypuklykh prostranstv, vazhnykh v prilozheniyakh”, Matematika, 1:1 (1957), 60–77

[17] Raikov D. A., “O dvukh klassakh lokalno vypuklykh prostranstv, vazhnykh v prilozheniyakh”, Tr. seminara po funkts. analizu, 5, Voronezh, 1957, 22–34 | MR

[18] Baernstein A., “Representation of holomorphic functions by boundary integrals”, Trans. Amer. Math. Soc., 160 (1971), 27–37 | DOI | MR | Zbl

[19] Levin B. Ya., Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956, 632 pp.

[20] Martineau A., “Équation différentielles d'ordre infini”, Bull. Soc. Math. Franc., 95 (1967), 109–154 | MR | Zbl

[21] Edvards R., Funktsionalnyi analiz, Mir, M., 1969, 1072 pp.