Geodesic
Classification of $H^2$-functions according to the degree of their cyclicity
Izvestiya. Mathematics , Tome 23 (1984) no. 2, pp. 225-242

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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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     author = {V. I. Vasyunin and N. K. Nikol'skii},
     title = {Classification of $H^2$-functions according to the degree of their cyclicity},
     journal = {Izvestiya. Mathematics },
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     number = {2},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1984_23_2_a1/}
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V. I. Vasyunin; N. K. Nikol'skii. Classification of $H^2$-functions according to the degree of their cyclicity. Izvestiya. Mathematics , Tome 23 (1984) no. 2, pp. 225-242. http://geodesic.mathdoc.fr/item/IM2_1984_23_2_a1/