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Mat. Sb. (N.S.), 1978, Volume 105(147), Number 2, Pages 238–260 (Mi msb2521)  

This article is cited in 3 scientific papers (total in 3 papers)

Some bases in spaces of regular functions and their application to interpolation

V. A. Oskolkov


Abstract: Systems of functions $\{\underset tL _n[\Phi(tz)]\}_0^\infty$ are considered, where $\Phi(z)=\sum_0^\infty a_nz^n$ ($a_n\ne0$, $n=0,1,…$) is an entire function,
$$ L_n[F]=\frac{n!}{2\pi i}\int_{|z|=r_n>\max\limits_{0\leqslant k\leqslant n}|\lambda_{k,n}|}\frac{F(z) dz}{(z-\lambda_{0,n})\cdots (z-\lambda_{n,n})}\qquad(n=0,1,…), $$
and the matrix $(\lambda_{k,n})$, $k=0,1,…,n$, $n=0,1,…$, is given.
Under various assumptions on the matrix, theorems are proved which deal with the question of whether the systems $\{\underset tL _n[\Phi(tz)]\}_0^\infty$ form a basis in the spaces $A(|z|<R)$. They are conclusive in the sense that they cannot be improved without changing the hypotheses.
The basis theorems are applied to Gel'fond and Abel–Goncharov interpolation problems, which makes it possible to study the distribution of zeros of sequences of derivatives of certain classes of entire functions.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1978, 34:2, 215–234

Bibliographic databases:

UDC: 517.535.4
MSC: Primary 30H05, 30E05; Secondary 30D20, 30C15
Received: 06.07.1976

Citation: V. A. Oskolkov, “Some bases in spaces of regular functions and their application to interpolation”, Mat. Sb. (N.S.), 105(147):2 (1978), 238–260; Math. USSR-Sb., 34:2 (1978), 215–234

Citation in format AMSBIB
\Bibitem{Osk78}
\by V.~A.~Oskolkov
\paper Some bases in spaces of regular functions and their application to interpolation
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 105(147)
\issue 2
\pages 238--260
\mathnet{http://mi.mathnet.ru/msb2521}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=489653}
\zmath{https://zbmath.org/?q=an:0421.30040}
\transl
\jour Math. USSR-Sb.
\yr 1978
\vol 34
\issue 2
\pages 215--234
\crossref{https://doi.org/10.1070/SM1978v034n02ABEH001157}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. V. A. Oskolkov, “On some questions in the theory of entire functions”, Russian Acad. Sci. Sb. Math., 78:1 (1994), 113–129  mathnet  crossref  mathscinet  zmath  isi
    3. A. Yu. Popov, “Bounds for convergence and uniqueness in Abel–Goncharov interpolation problems”, Sb. Math., 193:2 (2002), 247–277  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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