Absolute completeness of systems of exponentials on convex compact sets
Sbornik. Mathematics, Tome 196 (2005) no. 12, pp. 1801-1814 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Approximation using linear combinations of exponentials with special constraints on the coefficients is investigated. A sufficient condition for such approximation is stated in simple geometric terms.
@article{SM_2005_196_12_a2,
     author = {I. F. Krasichkov-Ternovskii and G. N. Shilova},
     title = {Absolute completeness of systems of exponentials on convex compact sets},
     journal = {Sbornik. Mathematics},
     pages = {1801--1814},
     year = {2005},
     volume = {196},
     number = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_12_a2/}
}
TY  - JOUR
AU  - I. F. Krasichkov-Ternovskii
AU  - G. N. Shilova
TI  - Absolute completeness of systems of exponentials on convex compact sets
JO  - Sbornik. Mathematics
PY  - 2005
SP  - 1801
EP  - 1814
VL  - 196
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/SM_2005_196_12_a2/
LA  - en
ID  - SM_2005_196_12_a2
ER  - 
%0 Journal Article
%A I. F. Krasichkov-Ternovskii
%A G. N. Shilova
%T Absolute completeness of systems of exponentials on convex compact sets
%J Sbornik. Mathematics
%D 2005
%P 1801-1814
%V 196
%N 12
%U http://geodesic.mathdoc.fr/item/SM_2005_196_12_a2/
%G en
%F SM_2005_196_12_a2
I. F. Krasichkov-Ternovskii; G. N. Shilova. Absolute completeness of systems of exponentials on convex compact sets. Sbornik. Mathematics, Tome 196 (2005) no. 12, pp. 1801-1814. http://geodesic.mathdoc.fr/item/SM_2005_196_12_a2/

[1] Davis Ph., Fan Ky., “Complete sequences and approximation in normed linear spaces”, Duke Math. J., 24:2 (1957), 183–192 | DOI | MR | Zbl

[2] Khavinson S. Ya., “Nekotorye voprosy polnoty sistem”, Dokl. AN SSSR, 137:4 (1961), 793–796 | Zbl

[3] Stafney J. A., “A permissible restriction on the coefficients in uniform polynomial approximation to $C[0,1]$”, Duke Math. J., 3:3 (1967), 393–396 | DOI | MR

[4] Khavinson S. Ya., “Dopustimye velichiny koeffitsientov mnogochlenov pri ravnomernoi approksimatsii nepreryvnykh funktsii”, Matem. zametki, 6:5 (1969), 619–625 | MR | Zbl

[5] Khavinson S. Ya., “O ponyatii polnoty, uchityvayuschei velichiny koeffitsientov approksimiruyuschikh polinomov”, Izv. AN ArmSSR. Ser. matem., 6:2–3 (1971), 221–233

[6] Gurarii V. I., Meletidi M. A., “Ob otsenkakh koeffitsientov polinomov, approksimiruyuschikh nepreryvnye funktsii”, Funkts. analiz i ego prilozh., 5:1 (1971), 73–75 | MR | Zbl

[7] Muradyan O. A., “O roste koeffitsientov approksimiruyuschikh agregatov v teoreme Myuntsa”, Izv. AN ArmSSR. Ser. matem., 8:1 (1973), 70–87 | MR

[8] Muradyan O. A., Khavinson S. Ya., “O velichinakh koeffitsientov mnogochlenov v approksimatsionnoi teoreme Veiershtrassa”, Matem. zametki, 22:2 (1977), 269–276 | MR | Zbl

[9] Golitschek M., Leviatan D., “Permissible bounds on the coeffitients of approximating polynomials with real or complex exponents”, J. Math. Anal. Appl., 60:1 (1977), 123–128 | DOI | MR

[10] Trigub R. M., “O priblizhenii funktsii mnogochlenami so spetsialnymi koeffitsientami”, Izv. vuzov. Ser. matem., 1977, no. 1, 93–99 | MR | Zbl

[11] Napalkov V. V., “Approksimatsiya funktsii mnogikh peremennykh s uchetom rosta koeffitsientov approksimiruyuschikh agregatov”, Matem. sb., 111:1 (1980), 144–156 | MR | Zbl

[12] Krasichkov-Ternovskii I. F., “Ob absolyutnoi polnote sistemy eksponent na intervale”, Matem. sb., 131(173):3(11) (1986), 309–322 | MR | Zbl

[13] Khavinson S. Ya., “Ob ekstremalnykh zadachakh dlya funktsii, udovletvoryayuschikh dopolnitelnym ogranicheniyam vnutri oblasti, i primenenie etikh zadach k voprosam approksimatsii”, Dokl. AN SSSR, 135:2 (1960), 270–273 | Zbl

[14] Khavinson S. Ya., “Ob approksimatsii s uchetom velichin koeffitsientov approksimiruyuschikh agregatov”, Trudy MIAN, 60, 1961, 304–324 | MR | Zbl

[15] Pólya G., “Untersuchuqen über Lücken und Singularitäten von Potenzreihen”, Math. Z., 29 (1929), 549–640 | DOI | MR

[16] Pasechnik G. M., “Geometricheskaya kharakterizatsiya mnozhestva pokazatelei predstavlyayuschei sistemy eksponent dlya prostranstva $H(G)$”, Dokl. AN SSSR, 252:3 (1980), 553–555 | MR | Zbl

[17] Levin B. Ya., Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956

[18] Shilova G. N., “Teorema o delitelyakh tselykh funktsii konechnogo poryadka”, Matem. zametki, 48:2 (1990), 128–136 | MR | Zbl

[19] Pfluger A., “Die Wertverteilung und das Verhalten von Betrag und Argument einer speziellen Klasse analytischer Funktion. I”, Comment Math. Helv., 11 (1938), 180–213 | DOI | MR

[20] Pfluger A., “Die Wertverteilung und das Verhalten von Betrag und Argument einer speziellen Klasse analytischer Funktion. II”, Comment Math. Helv., 12 (1939), 25–69 | DOI | MR