Asymptotics of singular numbers of imbedding operators for certain classes of analytic functions
Sbornik. Mathematics, Tome 43 (1982) no. 4, pp. 563-571 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This article is a detailed exposition of the results in the author's note “Asymptotic behavior of singular numbers of integral operators with Cauchy kernels and Bergman kernels”, Funkts. Analiz, 1978, vol. 12, No. 2, p. 88. Bibliography: 13 titles.
@article{SM_1982_43_4_a7,
     author = {O. G. Parfenov},
     title = {Asymptotics of singular numbers of imbedding operators for certain classes of analytic functions},
     journal = {Sbornik. Mathematics},
     pages = {563--571},
     year = {1982},
     volume = {43},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1982_43_4_a7/}
}
TY  - JOUR
AU  - O. G. Parfenov
TI  - Asymptotics of singular numbers of imbedding operators for certain classes of analytic functions
JO  - Sbornik. Mathematics
PY  - 1982
SP  - 563
EP  - 571
VL  - 43
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1982_43_4_a7/
LA  - en
ID  - SM_1982_43_4_a7
ER  - 
%0 Journal Article
%A O. G. Parfenov
%T Asymptotics of singular numbers of imbedding operators for certain classes of analytic functions
%J Sbornik. Mathematics
%D 1982
%P 563-571
%V 43
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1982_43_4_a7/
%G en
%F SM_1982_43_4_a7
O. G. Parfenov. Asymptotics of singular numbers of imbedding operators for certain classes of analytic functions. Sbornik. Mathematics, Tome 43 (1982) no. 4, pp. 563-571. http://geodesic.mathdoc.fr/item/SM_1982_43_4_a7/

[1] Parfenov O. G., “Asimptotika singulyarnykh chisel integralnykh operatorov s yadrami Koshi i Bergmana”, Funkts. analiz, 12:2 (1978), 88 | MR | Zbl

[2] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR

[3] Aronshain N., “Teoriya vosproizvodyaschikh yader”, Matematika, 7:2 (1963), 67–130

[4] Zakharyuta V. P., Skiba N. I., “Otsenki $n$-poperechnikov nekotorykh klassov funktsii, analiticheskikh na rimanovykh poverkhnostyakh”, Matem. zametki, 19:6 (1976), 899–911 | MR | Zbl

[5] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965 | MR

[6] Parfenov O. G., Asimptotika singulyarnykh chisel integralnykh operatorov s yadrom Koshi i ee sledstviya, Dep. v VINITI ot 14 iyulya 1978, No 2405-78 | Zbl

[7] Khvedelidze B. V., “Metod integralov tipa Koshi v razryvnykh zadachakh teorii golomorfnykh funktsii odnogo kompleksnogo peremennogo”, Itogi nauki i tekhniki. Sovremennye problemy matematiki, 7, VINITI, M., 1975, 5–162

[8] Erokhin V. D., “O nailuchshei lineinoi approksimatsii funktsii, analiticheski prodolzhimykh s dannogo kontinuuma v dannuyu oblast”, UMN, XXIII:1 (1968), 91–132

[9] Ramm A. G., “O sobstvennykh chislakh nekotorykh integralnykh operatorov”, Diff. uravneniya, 14:5 (1978), 932–934 | MR | Zbl

[10] Suetin P. K., “Polinomy, ortogonalnye po ploschadi i polinomy Biberbakha”, Trudy matem. in-ta im. V. A. Steklova, 1971, 1–86

[11] Paatashvili B. A., “O prinadlezhnosti klassam $E^p$ analiticheskikh funktsii, predstavimykh integralami tipa Koshi”, Trudy Tbilissk. matem. in-ta AN Gruz. SSR, 42 (1972), 87–94 | Zbl

[12] Ulyanov P. L., “Ob integralakh tipa Koshi”, Trudy matem. in-ta im. V. A. Steklova, LX (1961), 262–281 | MR | Zbl

[13] Petrovskii I. G., Lektsii po teorii integralnykh uravnenii, Nauka, M., 1965 | MR | Zbl