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

This article is cited in 4 scientific papers (total in 4 papers)

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
Received: 20.04.1974

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Michael Meyer, “Trianguläre interpolation”, Mh Math, 97:4 (1984), 287  crossref  mathscinet  zmath  isi
    2. F Haslinger, M Meyer, “Abel-Gončarov approximation and interpolation”, Journal of Mathematical Analysis and Applications, 110:2 (1985), 340  crossref
    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  mathnet  crossref  mathscinet  zmath  isi
    4. M. Maldonado, J. Prada, “Weighted shift operators on Köthe spaces”, Math Nachr, 279:1-2 (2006), 188  crossref  mathscinet  zmath  isi
  • Успехи математических наук Russian Mathematical Surveys
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