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 Uspekhi Mat. Nauk, 1975, Volume 30, Issue 6(186), Pages 101–146 (Mi umn4290)

The matrix method and quasi-power bases in the space of analytic functions in a disc

I. I. Ibragimov, N. I. Nagnibida

Abstract: We denote by $A_R(0<R\leqslant\infty)$ the space of all single-valued functions analytic in the disc $|z|<R$, with the topology of compact convergence. In the paper we present a survey of the results obtained during the last twenty years from investigations (using the matrix description of continuous linear operators) of conditions for systems of analytic functions to be quasi-power bases in $A_R$. We treat applications to many classical systems of functions and to systems formed from solutions of certain differential equations.

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English version:
Russian Mathematical Surveys, 1975, 30:6, 107–154

Bibliographic databases:

UDC: 517.537
MSC: 47A56, 47B38, 46A19, 47E05

Citation: I. I. Ibragimov, N. I. Nagnibida, “The matrix method and quasi-power bases in the space of analytic functions in a disc”, Uspekhi Mat. Nauk, 30:6(186) (1975), 101–146; Russian Math. Surveys, 30:6 (1975), 107–154

Citation in format AMSBIB
\Bibitem{IbrNag75} \by I.~I.~Ibragimov, N.~I.~Nagnibida \paper The matrix method and quasi-power bases in the space of analytic functions in a~disc \jour Uspekhi Mat. Nauk \yr 1975 \vol 30 \issue 6(186) \pages 101--146 \mathnet{http://mi.mathnet.ru/umn4290} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=435814} \zmath{https://zbmath.org/?q=an:0329.46021|0337.46025} \transl \jour Russian Math. Surveys \yr 1975 \vol 30 \issue 6 \pages 107--154 \crossref{https://doi.org/10.1070/RM1975v030n06ABEH001533} 

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This publication is cited in the following articles:
1. Michael Meyer, “Trianguläre interpolation”, Mh Math, 97:4 (1984), 287
2. F Haslinger, M Meyer, “Abel-Gončarov approximation and interpolation”, Journal of Mathematical Analysis and Applications, 110:2 (1985), 340
3. V. A. Oskolkov, “On the completeness and quasipower basis property of systems $ż^nf(\lambda_nz)\}$”, Math. USSR-Sb., 66:2 (1990), 383–392
4. M. Maldonado, J. Prada, “Weighted shift operators on Köthe spaces”, Math Nachr, 279:1-2 (2006), 188
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