Geodesic
A criterion for the solvability of nonhomogeneous convolution equations in convex domains of the space $\mathbf C^n$
Izvestiya. Mathematics , Tome 36 (1991) no. 3, pp. 497-517.

Voir la notice de l'article provenant de la source Math-Net.Ru

A criterion is given, in terms of the Laplace transform of an analytic functional , for the convolution operator $M_u\colon H(\mathscr D+k)\to H(\mathscr D)$, corresponding to this functional, to be an epimorphism, in the case when $\mathscr D$ is an arbitrary convex domain and $K$ an arbitrary convex compact set in $\mathbf C^n$. 
@article{IM2_1991_36_3_a2,
     author = {A. S. Krivosheev},
     title = {A criterion for the solvability of nonhomogeneous convolution equations in convex domains of the space $\mathbf C^n$},
     journal = {Izvestiya. Mathematics },
     pages = {497--517},
     publisher = {mathdoc},
     volume = {36},
     number = {3},
     year = {1991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_36_3_a2/}
}
TY  - JOUR
AU  - A. S. Krivosheev
TI  - A criterion for the solvability of nonhomogeneous convolution equations in convex domains of the space $\mathbf C^n$
JO  - Izvestiya. Mathematics 
PY  - 1991
SP  - 497
EP  - 517
VL  - 36
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1991_36_3_a2/
LA  - en
ID  - IM2_1991_36_3_a2
ER  - 
%0 Journal Article
%A A. S. Krivosheev
%T A criterion for the solvability of nonhomogeneous convolution equations in convex domains of the space $\mathbf C^n$
%J Izvestiya. Mathematics 
%D 1991
%P 497-517
%V 36
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1991_36_3_a2/
%G en
%F IM2_1991_36_3_a2
A. S. Krivosheev. A criterion for the solvability of nonhomogeneous convolution equations in convex domains of the space $\mathbf C^n$. Izvestiya. Mathematics , Tome 36 (1991) no. 3, pp. 497-517. http://geodesic.mathdoc.fr/item/IM2_1991_36_3_a2/

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

[2] Napalkov V. V., “Ob odnom klasse neodnorodnykh uravnenii tipa svertki”, UMN, 29:3 (1974), 217–218 | MR | Zbl

[3] Epifanov O. V., “Ob epimorfizme svertki v vypuklykh oblastyakh”, DAN SSSR, 217:1 (1974), 18–19 | MR | Zbl

[4] Malgrange B., “Existence et approximation des solutions des equations aux dérivées partielles et des équations de convolution”, Ann. Inst. Fourier, 56:6 (1955), 271–354 | MR

[5] Martineau A., “Equations differentielles d'ordre infini”, Bull. Soc. Math. France, 1967, no. 95, 109–154 | MR | Zbl

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

[7] Morzhakov V. V., “Ob uravneniyakh svertki v prostranstvakh funktsii, golomorfnykh v vypuklykh oblastyakh i na vypuklykh kompaktakh v $\mathbf{C}^n$”, Matem. zametki, 16:3 (1974), 431–440 | Zbl

[8] Morzhakov V. V., “Ob epimorfizme operatora svertki v vypuklykh oblastyakh v $\mathbf{C}^n$”, Matematicheskii analiz i ego prilozheniya, Rostov-na-Donu, 1985, 91–99 | MR | Zbl

[9] Morzhakov V. V., “Ob epimorfnosti operatora svertki v vypuklykh oblastyakh iz $\mathbf{C}^n$”, Matem. sb., 132(174):3 (1987), 352–370 | MR | Zbl

[10] Ronkin L. I., Vvedenie v teoriyu tselykh funktsii mnogikh peremennykh, Nauka, M., 1971 | MR | Zbl

[11] Lelong P., Gruman L., Entire functions of several complex variables, Springer, Berlin, 1986 | MR

[12] Leikhtveis K., Vypuklye mnozhestva, Nauka, M., 1985 | MR

[13] Favorov S. Yu., “O slozhenii indikatorov tselykh i subgarmonicheskikh funktsii mnogikh peremennykh”, Matem. sb., 105(147):1 (1978), 128–140 | MR | Zbl

[14] Sigurdsson R., Growth properties of analytic and plurisubharmonic functions of finite order, Dis. $\dots$ Dokt., University of Lund and Lund institute of technology, 1984

[15] Sekerin A. B., Predstavlenie funktsii kratnymi ryadami eksponent, Dis. $\dots$ kand. fiz.-matem. nauk, RGU, Rostov-na-Donu, 1982

[16] Morzhakov V. V., “Uravneniya svertki v vypuklykh oblastyakh iz $\mathbf{C}^n$ s negladkoi granitsei”, IV Mezhdunar. konf. po kompleksnomu analizu i prilozheniyam, Tez. dokladov, Varna, 1987, 115