Geodesic
Spectral synthesis for the differentiation operator on systems of curvilinear strips
Sbornik. Mathematics, Tome 186 (1995) no. 5, pp. 711-728 
S. G. Merzlyakov. Spectral synthesis for the differentiation operator on systems of curvilinear strips. Sbornik. Mathematics, Tome 186 (1995) no. 5, pp. 711-728. http://geodesic.mathdoc.fr/item/SM_1995_186_5_a4/
@article{SM_1995_186_5_a4,
     author = {S. G. Merzlyakov},
     title = {Spectral synthesis for the~differentiation operator on systems of curvilinear strips},
     journal = {Sbornik. Mathematics},
     pages = {711--728},
     year = {1995},
     volume = {186},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_5_a4/}
}
TY  - JOUR
AU  - S. G. Merzlyakov
TI  - Spectral synthesis for the differentiation operator on systems of curvilinear strips
JO  - Sbornik. Mathematics
PY  - 1995
SP  - 711
EP  - 728
VL  - 186
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/SM_1995_186_5_a4/
LA  - en
ID  - SM_1995_186_5_a4
ER  - 
%0 Journal Article
%A S. G. Merzlyakov
%T Spectral synthesis for the differentiation operator on systems of curvilinear strips
%J Sbornik. Mathematics
%D 1995
%P 711-728
%V 186
%N 5
%U http://geodesic.mathdoc.fr/item/SM_1995_186_5_a4/
%G en
%F SM_1995_186_5_a4

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

Let $G_1,\dots,G_q$ be curvilinear strips in the complex plane, and $H(G_1),\dots,H(G_q)$ the spaces of holomorphic functions in the domains $G_1,\dots,G_q$, respectively, endowed with the usual topology of uniform convergence on compact sets. Denote the topological product $H=H(G_1)\times\dots\times H(G_q)$ by $H$. In this paper the structure of closed subspaces of $H$ that are invariant under the action of the operator of componentwise differentiation is investigated.

[1] Krasichkov-Ternovskii I. F., “Invariantnye podprostranstva analiticheskikh funktsii. 1: Spektralnyi sintez na vypuklykh oblastyakh”, Matem. sb., 87 (1972), 459–489 | MR

[2] Krasichkov-Ternovskii I. F., “Invariantnye podprostranstva analiticheskikh funktsii. 2: Spektralnyi sintez na vypuklykh oblastyakh”, Matem. sb., 88 (1972), 3–30

[3] Krasichkov-Ternovskii I. F., “Invariantnye podprostranstva analiticheskikh funktsii. 3: O rasprostranenii spektralnogo sinteza”, Matem. sb., 88 (1972), 331–352 | MR

[4] Krasichkov-Ternovskii I. F., “Spektralnyi sintez na sistemakh vypuklykh oblastei”, Matem. sb., 111:1 (1980), 3–41 | MR

[5] Krasichkov-Ternovskii I. F., “Spektralnyi sintez na sistemakh neogranichennykh vypuklykh oblastei”, Matem. sb., 111:3 (1980), 384–401 | MR

[6] Krasichkov-Ternovskii I. F., “Spektralnyi sintez na sistemakh vypuklykh oblastei. Rasprostranenie sinteza”, Matem. sb., 112:1 (1980), 94–114 | MR

[7] Leontev A. F., Posledovatelnosti polinomov iz eksponent, Nauka, M., 1980 | MR

[8] Kote G., “Dualitat in der Functionentheorie”, J. reine und angew. Math., 191:1–2 (1953), 30–49 | MR

[9] Aronszajn N., “Sur les decompositions des fonctions analytiques uniformes et sur leurs applications”, Acta Math., 65:1–2 (1935), 381–400 | MR

[10] Leontev A. F., Ryady eksponent, Nauka, M., 1976 | MR

[11] Gelfond A. O., Ischislenie konechnykh raznostei, Nauka, M., 1967 | MR

[12] Merzlyakov S. G., “Teorema tipa Runge dlya invariantnykh podprostranstv”, Issledovaniya po kompleksnomu analizu, BFAN SSSR, Ufa, 1987, 121–128

[13] Korobeinik Yu. F., “Suschestvovanie analiticheskogo resheniya differentsialnogo uravneniya beskonechnogo poryadka i kharakter ego oblasti analitichnosti”, Matem. sb., 80:1 (1969), 52–76 | MR | Zbl

[14] Leontev A. F., “Ryady polinomov Dirikhle i ikh obobscheniya”, Tr. MIAN, 39, Nauka, M., 1951, 3–214 | MR | Zbl

[15] Merzlyakov S. G., “Invariantnye podprostranstva operatora edinichnogo sdviga”, Izv. RAN. Ser. matem., 56:6 (1992), 1244–1272 | MR | Zbl