Geodesic
Spectral synthesis in certain spaces of entire functions of exponential type and its applications
Izvestiya. Mathematics , Tome 64 (2000) no. 4, pp. 777-786.

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

We consider certain spaces $P_\Omega$ of entire functions of exponential type in $\mathbb C^n$ associated with a domain $\Omega\in\mathbb R^n$ that are in fact Laplace transforms of distributions in $\Omega$. It is shown that any shift-invariant subspace of these functions admits spectral synthesis, that is, coincides with the closure of the linear span of the exponential polynomials contained in it. As an application of this result, we describe the solution space in $P_\Omega$ of a system of homogeneous equations of infinite order for differential operators with characteristic functions infinitely differentiable in $\Omega$. 
@article{IM2_2000_64_4_a3,
     author = {O. V. Odinokov},
     title = {Spectral synthesis in certain spaces of entire functions of exponential type and its applications},
     journal = {Izvestiya. Mathematics },
     pages = {777--786},
     publisher = {mathdoc},
     volume = {64},
     number = {4},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2000_64_4_a3/}
}
TY  - JOUR
AU  - O. V. Odinokov
TI  - Spectral synthesis in certain spaces of entire functions of exponential type and its applications
JO  - Izvestiya. Mathematics 
PY  - 2000
SP  - 777
EP  - 786
VL  - 64
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2000_64_4_a3/
LA  - en
ID  - IM2_2000_64_4_a3
ER  - 
%0 Journal Article
%A O. V. Odinokov
%T Spectral synthesis in certain spaces of entire functions of exponential type and its applications
%J Izvestiya. Mathematics 
%D 2000
%P 777-786
%V 64
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2000_64_4_a3/
%G en
%F IM2_2000_64_4_a3
O. V. Odinokov. Spectral synthesis in certain spaces of entire functions of exponential type and its applications. Izvestiya. Mathematics , Tome 64 (2000) no. 4, pp. 777-786. http://geodesic.mathdoc.fr/item/IM2_2000_64_4_a3/

[1] Khermander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, T. 1, Mir, M., 1986

[2] Filippov V. N., “Spektralnyi sintez v nekotorykh prostranstvakh tselykh funktsii eksponentsialnogo tipa”, Matem. zametki, 30:4 (1981), 527–534 | MR | Zbl

[3] Dubinskii Yu. A., “Algebra psevdodifferentsialnykh operatorov s kompleksnymi argumentami i ee prilozheniya”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Noveishie dostizheniya, 29, VINITI AN SSSR, M., 1986, 109–150 | MR

[4] Shilov G. E., Matematicheskii analiz. Vtoroi spetsialnyi kurs, Izd-vo MGU, M., 1984 | MR | Zbl

[5] Odinokov O. V., “Integralnoe predstavlenie tselykh funktsii i differentsialnye operatory beskonechnogo poryadka”, Izv. RAN. Ser. matem., 59:4 (1995), 179–186 | MR | Zbl

[6] Edvards R., Funktsionalnyi analiz, Mir, M., 1969

[7] Komatsu H., “Ultradistributions, I”, J. Fac. Sci. Univ. Tokyo. Sec. IA, 20:1 (1973), 25–105 | MR | Zbl

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

[9] Malgranzh B., Idealy differentsiruemykh funktsii, Mir, M., 1968