Geodesic
The multipoint de la Vallée-Poussin problem for a convolution operator
Sbornik. Mathematics, Tome 203 (2012) no. 2, pp. 224-233 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Conditions are discovered which ensure that the space of entire functions can be represented as the sum of an ideal in the space of entire functions and the kernel of a convolution operator. In this way conditions for the multipoint de la Vallée-Poussin problem to have a solution are found. Bibliography: 14 titles.
Keywords: convolution operator, Fischer pairs
Mots-clés : multipoint de la Vallée-Poussin problem. 
@article{SM_2012_203_2_a3,
     author = {V. V. Napalkov and A. A. Nuyatov},
     title = {The multipoint de la {Vall\'ee-Poussin} problem for a~convolution operator},
     journal = {Sbornik. Mathematics},
     pages = {224--233},
     year = {2012},
     volume = {203},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_2_a3/}
}
TY  - JOUR
AU  - V. V. Napalkov
AU  - A. A. Nuyatov
TI  - The multipoint de la Vallée-Poussin problem for a convolution operator
JO  - Sbornik. Mathematics
PY  - 2012
SP  - 224
EP  - 233
VL  - 203
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_2012_203_2_a3/
LA  - en
ID  - SM_2012_203_2_a3
ER  - 
%0 Journal Article
%A V. V. Napalkov
%A A. A. Nuyatov
%T The multipoint de la Vallée-Poussin problem for a convolution operator
%J Sbornik. Mathematics
%D 2012
%P 224-233
%V 203
%N 2
%U http://geodesic.mathdoc.fr/item/SM_2012_203_2_a3/
%G en
%F SM_2012_203_2_a3
V. V. Napalkov; A. A. Nuyatov. The multipoint de la Vallée-Poussin problem for a convolution operator. Sbornik. Mathematics, Tome 203 (2012) no. 2, pp. 224-233. http://geodesic.mathdoc.fr/item/SM_2012_203_2_a3/

[1] Ch. J. De La Vallée Poussin, “Sur l'équation différentielle linéaire du second ordre. Détermination d'une intégrale par deux valeurs assignées. Extension aux équations d'ordre $n$”, Journ. de Math. (9), 8 (1929), 125–144 | Zbl

[2] E. Fischer, “Über die Differentiationsprozesse der Algebra”, J. Math., 148 (1917), 1–78 | Zbl

[3] L. Ehrenpreis, Fourier analysis in several complex variables, Wiley, New York, 1970 | MR | Zbl

[4] V. V. Napalkov, S. V. Popenov, “The holomorphic Cauchy problem for the convolution operator in analytically uniform spaces, and Fisher expansions”, Dokl. Math., 64:3 (2001), 330–332 | MR | Zbl

[5] H. S. Shapiro, “An algebraic theorem of E. Fischer, and the holomorphic Goursat problem”, Bull. London Math. Soc., 21:6 (1989), 513–537 | DOI | MR | Zbl

[6] V. V. Napalkov, “Complex analysis and the Cauchy problem for convolution operators”, Proc. Steklov Inst. Math., 235 (2001), 158–161 | MR | Zbl

[7] V. V. Napalkov, Uravneniya svertki v mnogomernykh prostranstvakh, Nauka, M., 1982 | MR | Zbl

[8] V. V. Napalkov, “On discrete weakly sufficient sets in certain spaces of entire functions”, Math. USSR-Izv., 19:2 (1982), 349–357 | DOI | MR | Zbl | Zbl

[9] V. V. Napalkov, “The strict topology in certain weighted spaces of functions”, Math. Notes, 39:4 (1986), 291–296 | DOI | MR | Zbl

[10] H. Muggli, “Differentialgleichungen unendlich hoher Ordnung mit konstanten Koeffizienten”, Comment. Math. Helv., 11:1 (1938), 151–179 | DOI | MR | Zbl

[11] A. Meril, D. C. Struppa, “Equivalence of Cauchy problems for entire and exponential type functions”, Bull. London Math. Soc., 17:5 (1985), 469–473 | DOI | MR | Zbl

[12] J. Dieudonné, L. Schwartz, “La dualité dans les espaces $(\mathscr F)$ et $(\mathscr L \mathscr F)$”, Ann. Inst. Fourier Grenoble, 1 (1949), 61–101 | DOI | MR | Zbl

[13] O. V. Epifanov, “O suschestvovanii nepreryvnogo pravogo obratnogo operatora v odnom klasse lokalno vypuklykh prostranstv”, Izv. Sev.-Kavkaz. Nauchnogo tsentra vysshei shkoly. Ser. estestv. nauk, 3 (1991), 3–4 | MR | Zbl

[14] J. Sebastiã o e Silva, “Su certe classi di spazi localmente convessi importanti per le applicazioni”, Rend. Mat. e Appl. (5), 14 (1955), 388–410 | MR | Zbl