Geodesic
On the convolution operator on a~finite interval
Izvestiya. Mathematics , Tome 11 (1977) no. 3, pp. 583-611.

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

In this paper a convolution operator whose kernel is the Fourier transform of a rational function is studied on a finite interval. Criteria are found for completeness and basicity of the root system of such an operator. Bibliography: 9 titles. 
@article{IM2_1977_11_3_a6,
     author = {Yu. I. Lyubarskii},
     title = {On the convolution operator on a~finite interval},
     journal = {Izvestiya. Mathematics },
     pages = {583--611},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {1977},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1977_11_3_a6/}
}
TY  - JOUR
AU  - Yu. I. Lyubarskii
TI  - On the convolution operator on a~finite interval
JO  - Izvestiya. Mathematics 
PY  - 1977
SP  - 583
EP  - 611
VL  - 11
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1977_11_3_a6/
LA  - en
ID  - IM2_1977_11_3_a6
ER  - 
%0 Journal Article
%A Yu. I. Lyubarskii
%T On the convolution operator on a~finite interval
%J Izvestiya. Mathematics 
%D 1977
%P 583-611
%V 11
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1977_11_3_a6/
%G en
%F IM2_1977_11_3_a6
Yu. I. Lyubarskii. On the convolution operator on a~finite interval. Izvestiya. Mathematics , Tome 11 (1977) no. 3, pp. 583-611. http://geodesic.mathdoc.fr/item/IM2_1977_11_3_a6/

[1] Vorovich I. I., Yudovich V. I., “Udar kruglogo diska o zhidkost konechnoi glubiny”, Prikladnaya matematika i mekhanika, 21:4 (1957), 525–532

[2] Paltsev B. V., “Uravnenie svertki na konechnom intervale s yadrom, preobrazovanie Fure kotorogo – ratsionalnaya funktsiya”, Izv. AN SSSR. Ser. matem., 36 (1972), 591–634

[3] Krein M. G., “Integralnye uravneniya na polupryamoi s yadrom, zavisyaschim ot raznosti argumentov”, Uspekhi matem. nauk, 13:3 (1958), 3–120 | MR | Zbl

[4] Gurvits A., Kurant R., Teoriya funktsii, Nauka, M., 1968 | MR

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

[6] Dzyadyk V. K., “Ob usloviyakh skhodimosti ryadov Dirikhle na zamknutykh mnogougolnikakh”, Matem. sb., 95:4 (1974), 475–493

[7] Levin B. Ya., Lyubarskii Yu. I., “Interpolyatsiya tselymi funktsiyami spetsialnykh klassov i svyazannye s neyu razlozheniya v ryady eksponent”, Izv. AN SSSR. Ser. matem., 39 (1975), 657–702 | MR | Zbl

[8] Levin B. Ya., Tselye funktsii, MGU, 1971

[9] Khromov A. P., “Konechnomernye vozmuscheniya volterrovykh operatorov”, Dokl. AN SSSR, 209:2 (1973), 309–311 | Zbl