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

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[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