Geodesic
On roots of the multiple integration operator in the space of functions analytic in a disk
Izvestiya. Mathematics, Tome 13 (1979) no. 3, pp. 685-693 
N. I. Nagnibida. On roots of the multiple integration operator in the space of functions analytic in a disk. Izvestiya. Mathematics, Tome 13 (1979) no. 3, pp. 685-693. http://geodesic.mathdoc.fr/item/IM2_1979_13_3_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $A_R$ denote the space of all single-valued functions analytic in the disk $|z|$, $0$, with the topology of compact convergence, and let $J$, $J\cdot=\int_0^z\cdot\,d\xi$, be the integration operator on it. In the paper all continuous linear operators on $A_R$ which satisfy the condition $Y^p=J^p$, where $p$ is a fixed natural number, are found, and it is shown that for each of them there exists a one-to-one bicontinuous mapping $T$ of the space $A_R$ to itself which commutes with $J^p$ and satisfies $YT=TJ$. Bibliography: 8 titles.

[1] Nagnibida N. I., “O nekotorykh svoistvakh operatorov obobschennogo integrirovaniya v analiticheskom prostranstve”, Sib. matem. zh., 7:6 (1966), 1306–1318 | MR | Zbl

[2] Nagnibida N. I., “Izomorfizmy prostranstva analiticheskikh funktsii v kruge, perestanovochnye so stepenyu operatora integrirovaniya”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, vyp. 6, Khark. gos. un-t, 1968, 184–188 | MR

[3] Khaplanov M. G., “Lineinye preobrazovaniya analiticheskikh prostranstv”, Dokl. AN SSSR, 80:1 (1951), 21–24

[4] Gantmakher F. R., Teoriya matrits, GITTL, M., 1953

[5] Berezovskii N. I., Nagnibida N. I., “Resheniya odnogo operatornogo uravneniya v prostranstve analiticheskikh funktsii”, Matem. sb., Naukova dumka, Kiev, 1976, 104–107 | MR

[6] Kazmin Yu. A., “Polinomy Goncharova i voprosy predstavleniya analiticheskoi funktsii ryadom po pervoobraznym nekotoroi funktsii”, Vest. Mosk. gos. un-ta, Matem., mekh., 1962, no. 6, 9–19 | MR

[7] Sakhnovich L. A., “Spektralnyi analiz operatorov vida $Kf=\int_0^x f(t)k(x-t)dt$”, Izv. AN SSSR. Ser. matem., 22 (1958), 299–308

[8] Nagnibida N. I., “K voprosu o privedenii operatorov Volterra v analiticheskikh prostranstvakh k prosteishemu vidu”, Matem. zametki, 17:4 (1975), 625–630 | MR | Zbl