Geodesic
The Helly problem and best approximation in a space of continuous functions
Izvestiya. Mathematics, Tome 1 (1967) no. 3, pp. 623-637 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Equivalence is verified between the Helly problem in the theory of moments and the problem of best approximation by elements of subspaces of finite defect. The existence and uniqueness conditions for the solution of these problems in a space of continuous functions are investigated. 
@article{IM2_1967_1_3_a5,
     author = {A. L. Garkavi},
     title = {The {Helly} problem and best approximation in a space of continuous functions},
     journal = {Izvestiya. Mathematics},
     pages = {623--637},
     year = {1967},
     volume = {1},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1967_1_3_a5/}
}
TY  - JOUR
AU  - A. L. Garkavi
TI  - The Helly problem and best approximation in a space of continuous functions
JO  - Izvestiya. Mathematics
PY  - 1967
SP  - 623
EP  - 637
VL  - 1
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IM2_1967_1_3_a5/
LA  - en
ID  - IM2_1967_1_3_a5
ER  - 
%0 Journal Article
%A A. L. Garkavi
%T The Helly problem and best approximation in a space of continuous functions
%J Izvestiya. Mathematics
%D 1967
%P 623-637
%V 1
%N 3
%U http://geodesic.mathdoc.fr/item/IM2_1967_1_3_a5/
%G en
%F IM2_1967_1_3_a5
A. L. Garkavi. The Helly problem and best approximation in a space of continuous functions. Izvestiya. Mathematics, Tome 1 (1967) no. 3, pp. 623-637. http://geodesic.mathdoc.fr/item/IM2_1967_1_3_a5/

[1] Aleksandrov P. S., Uryson P. S., O kompaktnykh topologicheskikh prostranstvakh, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 31, 1950 | MR | Zbl

[2] Garkavi A. L., “O nailuchshem priblizhenii elementami beskonechnomernykh podprostranstv odnogo klassa”, Matem. sb., 62 (1963), 104–120 | MR | Zbl

[3] Garkavi A. L., “O edinstvennosti resheniya $L$-problemy momentov”, Izv. AN SSSR. Ser. matem., 28 (1964), 553–570 | MR | Zbl

[4] Garkavi A. L., “Approksimativnye svoistva podprostranstv konechnogo defekta v prostranstve nepreryvnykh funktsii”, Dokl. AN SSSR, 155 (1964), 513–516 | MR | Zbl

[5] Garkavi A. L., “Chebyshevskie podprostranstva konechnogo defekta v prostranstve summiruemykh funktsii”, Uch. zap. kafedry matematiki Orekhovo-Zuevskogo pedinstituta, 22:3 (1964), 5–11 | MR

[6] Danford N., Shvarts Dzh., Lineinye operatory, IL, M., 1962

[7] Singer I., “Some remarks on best approximation in normed linear spaces”, Rev. math. pures et appl., 6 (1961), 357–362 | MR | Zbl

[8] Zukhovitskii S. I., “O minimalnykh rasshireniyakh lineinykh funktsionalov v prostranstve nepreryvnykh funktsii”, Izv. AN SSSR. Ser. matem., 21 (1957), 409–422

[9] Phelps R. R., “Čebyšev subspaces of finite codimension in $C(X)$”, Pasif. J. Math., 13 (1963), 647–655 | MR | Zbl

[10] Helly E., “Über Systeme linearer Gleichungen mit unendlich vielen Unbekannten”, Monatsh. Math. Phys., 31 (1921), 60–91 | DOI | MR | Zbl