On division problem in nonradial weighted spaces of entire functions
Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 3, pp. 7-18 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the inductive weighted space $H_{u,v}^{1,\infty}$ of entire functions defined by a sequence of nonradial two-part weights $\{q_nu(|z|)+nv(|\operatorname{Im}z|)\}_{n=1}^\infty$, $0. Under an additional assumption on the function $v$, we establish the division theorem in $H_{u,v}^{1,\infty}$. We also obtain some results about sweepping out the masses of the subharmonic function $v(|\operatorname{Im}z|)$.
@article{VMJ_2013_15_3_a1,
     author = {D. A. Abanina and A. V. Kuzminova},
     title = {On division problem in nonradial weighted spaces of entire functions},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {7--18},
     year = {2013},
     volume = {15},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2013_15_3_a1/}
}
TY  - JOUR
AU  - D. A. Abanina
AU  - A. V. Kuzminova
TI  - On division problem in nonradial weighted spaces of entire functions
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2013
SP  - 7
EP  - 18
VL  - 15
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMJ_2013_15_3_a1/
LA  - ru
ID  - VMJ_2013_15_3_a1
ER  - 
%0 Journal Article
%A D. A. Abanina
%A A. V. Kuzminova
%T On division problem in nonradial weighted spaces of entire functions
%J Vladikavkazskij matematičeskij žurnal
%D 2013
%P 7-18
%V 15
%N 3
%U http://geodesic.mathdoc.fr/item/VMJ_2013_15_3_a1/
%G ru
%F VMJ_2013_15_3_a1
D. A. Abanina; A. V. Kuzminova. On division problem in nonradial weighted spaces of entire functions. Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 3, pp. 7-18. http://geodesic.mathdoc.fr/item/VMJ_2013_15_3_a1/

[1] Berenstein K., Struppa D., “Kompleksnyi analiz i uravneniya v svertkakh”, Itogi nauki i tekhn. Ser. Sovr. probl. mat. Fundam. napravleniya, 54, VINITI, M., 1989, 5–111 | MR | Zbl

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

[3] Hörmander L., “On the range of convolution operators”, Ann. Math., 76 (1962), 148–170 | DOI | MR | Zbl

[4] 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

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

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

[7] 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

[8] Korobeinik Yu. F., “Razreshimost uravnenii svertki v nekotorykh klassakh analiticheskikh funktsii”, Mat. zametki, 49:2 (1991), 74–83 | MR | Zbl

[9] Napalkov V. V., Rudakov I. A., “Operator svertki v prostranstve veschestvenno analiticheskikh funktsii”, Mat. zametki, 49:3 (1991), 57–65 | MR | Zbl

[10] Momm S., “Division problems in spaces of entire functions of finite order”, Lecture Notes in Pure and Appl. Math., 150, Dekker, N.Y., 1994, 435–457 | MR

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

[12] Meyer T., “Surjectivity of convolution operators on spaces of ultradifferentiable functions of Roumieu type”, Stud. Math., 125:2 (1997), 101–129 | MR | Zbl

[13] Roumieu C., “Ultra-distributions définies sur $\mathbb R^n$ et sur certaines classes de variétés différentiables”, J. Anal. Math., 10 (1962/1963), 153–192 | DOI | MR | Zbl

[14] Björck G., “Linear partial differential operators and generalized distributions”, Ark. Mat., 6 (1965), 351–407 | DOI | MR

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

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

[17] Abanin A. V., Abanina D. A., “Teorema deleniya v nekotorykh vesovykh prostranstvakh tselykh funktsii”, Vladikavk. mat. zhurn., 12:3 (2010), 3–20 | MR | Zbl

[18] Abanina D. A., “Razreshimost uravnenii svertki v prostranstvakh ultradifferentsiruemykh funktsii Berlinga normalnogo tipa na intervale”, Sib. mat. zhurn., 53:3 (2012), 477–494 | MR | Zbl

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

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

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