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Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 6, Pages 1426–1435 (Mi izv1980)  

On roots of the multiple integration operator in the space of functions analytic in a disk

N. I. Nagnibida


Abstract: Let $A_R$ denote the space of all single-valued functions analytic in the disk $|z|<R$, $0<R\leqslant\infty$, 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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English version:
Mathematics of the USSR-Izvestiya, 1979, 13:3, 685–693

Bibliographic databases:

UDC: 517.5
MSC: Primary 47G05; Secondary 46E10, 30H05
Received: 01.12.1977

Citation: N. I. Nagnibida, “On roots of the multiple integration operator in the space of functions analytic in a disk”, Izv. Akad. Nauk SSSR Ser. Mat., 42:6 (1978), 1426–1435; Math. USSR-Izv., 13:3 (1979), 685–693

Citation in format AMSBIB
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\by N.~I.~Nagnibida
\paper On roots of the multiple integration operator in the space of functions analytic in a~disk
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 6
\pages 1426--1435
\mathnet{http://mi.mathnet.ru/izv1980}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=522945}
\zmath{https://zbmath.org/?q=an:0431.47029|0414.47035}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 3
\pages 685--693
\crossref{https://doi.org/10.1070/IM1979v013n03ABEH002085}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JG49100008}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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