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Mat. Sb. (N.S.), 1973, Volume 91(133), Number 4(8), Pages 580–626 (Mi msb3328)  

This article is cited in 3 scientific papers (total in 4 papers)

Uniqueness theorems for analytic functions asymptotically representable by Dirichlet–Taylor series

M. M. Dzhrbashyan


Abstract: Dirichlet–Taylor series
$$ \sum^\infty_{j=1}d_je^{-\lambda_j s}s^{s_j-1} $$
are considered, where $\{d_j\}^\infty_1$ is a sequence of complex numbers, $\{\lambda_j\}^\infty_1$ is a nondecreasing sequence of positive numbers, and $s_j\geqslant1$ ($j\geqslant1$) is the number of times $\lambda_j$ occurs in the segment $\{\lambda_1,…,\lambda_j\}$.
An “adherence principle” is established for these series. As applications of this principle, uniqueness theorems are proved for analytic functions which are asymptotically representable by partial sums of Dirichlet–Taylor series in strips.
Bibliography: 16 titles.

Full text: PDF file (3700 kB)
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English version:
Mathematics of the USSR-Sbornik, 1973, 20:4, 603–649

Bibliographic databases:

UDC: 517.522.6
MSC: Primary 30A16, 30A84; Secondary 30A64, 30A86, 40G10, 30A80, 47G05, 30A04
Received: 01.03.1973

Citation: M. M. Dzhrbashyan, “Uniqueness theorems for analytic functions asymptotically representable by Dirichlet–Taylor series”, Mat. Sb. (N.S.), 91(133):4(8) (1973), 580–626; Math. USSR-Sb., 20:4 (1973), 603–649

Citation in format AMSBIB
\Bibitem{Dzh73}
\by M.~M.~Dzhrbashyan
\paper Uniqueness theorems for analytic functions asymptotically representable by Dirichlet--Taylor series
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 91(133)
\issue 4(8)
\pages 580--626
\mathnet{http://mi.mathnet.ru/msb3328}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=335761}
\zmath{https://zbmath.org/?q=an:0281.30005}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 20
\issue 4
\pages 603--649
\crossref{https://doi.org/10.1070/SM1973v020n04ABEH002002}


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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. N. U. Arakelian, A. G. Vitushkin, V. S. Vladimirov, A. A. Gonchar, “Mkhitar Mkrtichevich Dzhrbashyan (on his sixtieth birthday)”, Russian Math. Surveys, 34:2 (1979), 269–275  mathnet  crossref  mathscinet  zmath
    2. M. M. Dzhrbashyan, “A characterization of the closed linear spans of two families of incomplete systems of analitic functions”, Math. USSR-Sb., 42:1 (1982), 1–70  mathnet  crossref  mathscinet  zmath
    3. M Blambert, R Parvatham, “On the singularities of analytic functions defined by L-Dirichletian elements”, Journal of Mathematical Analysis and Applications, 82:1 (1981), 292  crossref  mathscinet  zmath
    4. M. M. Dzhrbashyan, V. M. Martirosyan, “Integral representations and best approximation by generalized polynomials in systems of Mittag-Leffler type”, Math. USSR-Izv., 23:3 (1984), 449–471  mathnet  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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