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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

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
\Bibitem{Nag78} \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}