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

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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. 
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     author = {N. I. Nagnibida},
     title = {On roots of the multiple integration operator in the space of functions analytic in a~disk},
     journal = {Izvestiya. Mathematics },
     pages = {685--693},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {1979},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1979_13_3_a7/}
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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/