Geodesic
Normal solvability of linear differential equations in the complex plane
Izvestiya. Mathematics , Tome 6 (1972) no. 2, pp. 445-466.

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

The operator $L_nY=A(z)Y'(z)+B(z)Y(z)$, where $A(z)$ and $B(z)$ are square $n$th order matrices, regular in a region $G$ of arbitrary connectivity, and $Y(z)$ is a single-column matrix, regular in $G$, is investigated. The operator $L_nY$ is shown to be normally solvable in the space $A^n(G)$ of single-column matrices regular in $G$, and in certain subspaces of $A^n(G)$, and its index is evaluated. 
@article{IM2_1972_6_2_a7,
     author = {Yu. F. Korobeinik},
     title = {Normal solvability of linear differential equations in the complex plane},
     journal = {Izvestiya. Mathematics },
     pages = {445--466},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_2_a7/}
}
TY  - JOUR
AU  - Yu. F. Korobeinik
TI  - Normal solvability of linear differential equations in the complex plane
JO  - Izvestiya. Mathematics 
PY  - 1972
SP  - 445
EP  - 466
VL  - 6
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1972_6_2_a7/
LA  - en
ID  - IM2_1972_6_2_a7
ER  - 
%0 Journal Article
%A Yu. F. Korobeinik
%T Normal solvability of linear differential equations in the complex plane
%J Izvestiya. Mathematics 
%D 1972
%P 445-466
%V 6
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1972_6_2_a7/
%G en
%F IM2_1972_6_2_a7
Yu. F. Korobeinik. Normal solvability of linear differential equations in the complex plane. Izvestiya. Mathematics , Tome 6 (1972) no. 2, pp. 445-466. http://geodesic.mathdoc.fr/item/IM2_1972_6_2_a7/

[1] Perron O., “Ueber diejenigen Integrale linearer Differentialgleichungen, welche an einer Unbeslimmtheitstelle bestimmt verhalten”, Math. Ann., 70 (1911), 1–32 | DOI | MR | Zbl

[2] Hilb E., “Ueber diejenigen Integrale linearer Differentialgleichungen, welche sich an einer Unbeslimmtheitstelle bestimmt verhalten”, Math. Ann., 82 (1921), 40–41 | DOI | MR

[3] Lettenmeyer F., “Ueber die an einer Unbeslimmtheitstelle regulären Lösungen eines Systemes homogener linearen Differentialgleichungen”, Bayer. Akad. Wiss. München Math.-Nat. Abt., 1926, 287–307 | Zbl

[4] Khartman F., Obyknovennye differentsialnye uravneniya, glava 4, dobavlenie, Mir, M., 1970 | MR | Zbl

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

[6] Krein M. G., Gokhberg I. Ts., “Osnovnye polozheniya o defektnykh chislakh, kornevykh chislakh i indeksakh lineinykh operatorov”, Uspekhi matem. nauk, 12:2(74) (1957), 43–118 | MR | Zbl

[7] Robertson A. P., Robertson V. Dzh., Topologicheskie vektornye prostranstva, Mir, M., 1967 | MR | Zbl

[8] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz v normirovannykh prostranstvakh, GIFML, M., 1959 | MR

[9] Uolsh Dzh. L., Interpolyatsiya i approksimatsiya ratsionalnymi funktsiyami v kompleksnoi oblasti, IIL, M., 1961 | MR

[10] Korobeinik Yu. F., Demchenko T. I., “O razreshimosti odnogo klassa differentsialnykh uravnenii beskonechnogo poryadka”, Sib. matem. zh., 8:6 (1967), 1321–1338 | MR

[11] Korobeinik Yu. F., “Normalno razreshimye operatory i differentsialnye uravneniya beskonechnogo poryadka”, Litovskii Matem. Sb., 11:3 (1971), 569–596 | MR | Zbl