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Mat. Sb. (N.S.), 1980, Volume 113(155), Number 4(12), Pages 520–537 (Mi msb2816)  

This article is cited in 5 scientific papers (total in 6 papers)

Asymptotics of Hadamard determinants and the convergence of rows of Padé approximants for sums of exponentials

A. I. Aptekarev


Abstract: The asymptotics of Hadamard determinants $\Delta_{n,m}$ (of dimension $m\times m$) for arbitrary fixed $m$ and $n\to\infty$ for the function $f(z)=\sum^k_{t=1}e^{\lambda_tz}$ are studied, where $\{\lambda_t\}^k_{t=1}$ are distinct complex numbers with unit modulus. A theorem on the convergence of the $(s\cdot p)$th row of the Padé table for the function $f(z)=\sum^k_{t=1}e^{\lambda_tz}$ ($\{\lambda_t\}^k_{t=1}$ are arbitrary distinct complex numbers) in the topology of $H(\mathbf C)$ holds for arbitrary natural numbers $p$ and $s$ equal to the number of $\lambda_t$ with modulus that is maximal among the $\{\lambda_t\}^k_{t=1}$.
Bibliography: 8 titles.

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English version:
Mathematics of the USSR-Sbornik, 1982, 41:4, 427–441

Bibliographic databases:

UDC: 517.53
MSC: Primary 41A21, 30E10; Secondary 15A15
Received: 21.12.1979

Citation: A. I. Aptekarev, “Asymptotics of Hadamard determinants and the convergence of rows of Padé approximants for sums of exponentials”, Mat. Sb. (N.S.), 113(155):4(12) (1980), 520–537; Math. USSR-Sb., 41:4 (1982), 427–441

Citation in format AMSBIB
\Bibitem{Apt80}
\by A.~I.~Aptekarev
\paper Asymptotics of Hadamard determinants and the convergence of rows of Pad\'e approximants for sums of exponentials
\jour Mat. Sb. (N.S.)
\yr 1980
\vol 113(155)
\issue 4(12)
\pages 520--537
\mathnet{http://mi.mathnet.ru/msb2816}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=602273}
\zmath{https://zbmath.org/?q=an:0478.30006|0462.30006}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 41
\issue 4
\pages 427--441
\crossref{https://doi.org/10.1070/SM1982v041n04ABEH002241}


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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. Lubinsky D.S., “Uniform convergence of rows of the Padé table for functions with smooth Maclaurin series coefficients”, Constr. Approx., 3:1 (1987), 307–330  crossref  mathscinet  zmath  isi
    2. Starovoitov A., Starovoitova N., “Behavior of the Lines in the Pade and Chebyshev Tables for the Sum of Exponents”, Dokl. Akad. Nauk Belarusi, 36:3-4 (1992), 202–204  mathscinet  isi
    3. A. P. Starovoitov, N. A. Starovoitova, “Asymptotic behaviour of the Hadamard determinants and the behaviour of the rows of the Padé and Chebyshev tables for a sum of exponentials”, Sb. Math., 187:2 (1996), 297–313  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. V. N. Rusak, A. P. Starovoitov, “Padé approximants for entire functions with regularly decreasing Taylor coefficients”, Sb. Math., 193:9 (2002), 1303–1332  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. A. P. Starovoitov, N. A. Starovoitova, “Padé approximants of the Mittag-Leffler functions”, Sb. Math., 198:7 (2007), 1011–1023  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. V. M. Buchstaber, V. N. Dubinin, V. A. Kaliaguine, B. S. Kashin, V. N. Sorokin, S. P. Suetin, D. N. Tulyakov, B. N. Chetverushkin, E. M. Chirka, A. A. Shkalikov, “Alexander Ivanovich Aptekarev (on his 60th birthday)”, Russian Math. Surveys, 70:5 (2015), 965–973  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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