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Izv. Akad. Nauk SSSR Ser. Mat., 1983, Volume 47, Issue 5, Pages 942–960 (Mi izv1432)  

Classification of $H^2$-functions according to the degree of their cyclicity

V. I. Vasyunin, N. K. Nikol'skii


Abstract: The vector-valued functions $f$ in the Hardy space $H^2(E)$ are classified according to their approximation capabilities with respect to the backward shift operator $S^*$, $S^*f\overset{\operatorname{def}}=\frac{f-f(0)}z$, i.e., according to the “size” of the closed linear span $\operatorname{span}(S^{*k}f:k\geqslant0)$.
Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1984, 23:2, 225–242

Bibliographic databases:

UDC: 513.88
MSC: Primary 30D55, 47B37; Secondary 30D50, 30G30
Received: 19.01.1982

Citation: V. I. Vasyunin, N. K. Nikol'skii, “Classification of $H^2$-functions according to the degree of their cyclicity”, Izv. Akad. Nauk SSSR Ser. Mat., 47:5 (1983), 942–960; Math. USSR-Izv., 23:2 (1984), 225–242

Citation in format AMSBIB
\Bibitem{VasNik83}
\by V.~I.~Vasyunin, N.~K.~Nikol'skii
\paper Classification of $H^2$-functions according to the degree of their cyclicity
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1983
\vol 47
\issue 5
\pages 942--960
\mathnet{http://mi.mathnet.ru/izv1432}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=718412}
\zmath{https://zbmath.org/?q=an:0598.46033}
\transl
\jour Math. USSR-Izv.
\yr 1984
\vol 23
\issue 2
\pages 225--242
\crossref{https://doi.org/10.1070/IM1984v023n02ABEH001465}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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