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Izv. Akad. Nauk SSSR Ser. Mat., 1967, Volume 31, Issue 1, Pages 87–102 (Mi izv2530)  

This article is cited in 2 scientific papers (total in 3 papers)

Summability of the Dirichlet series with real exponents for an arbitrary analytic function

A. F. Leont'ev


Abstract: Given a function $f(z)$ that is analytic on a closed vertical interval of length $2\pi\sigma$, we use a definite rule to associate with it a formal Dirichlet series with exponents $\pm\lambda_n(n=1,2,…)$, where $\lambda_n>0$ and $\lim\limits_{n\to\infty}\frac{n}{\lambda_n}=\sigma$. In general this series diverges everywhere. We give a method for summing it to the function $f(z)$.

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English version:
Mathematics of the USSR-Izvestiya, 1967, 1:1, 81–94

Bibliographic databases:

UDC: 517.5
MSC: 30B50, 40A05, 40G10
Received: 17.03.1966

Citation: A. F. Leont'ev, “Summability of the Dirichlet series with real exponents for an arbitrary analytic function”, Izv. Akad. Nauk SSSR Ser. Mat., 31:1 (1967), 87–102; Math. USSR-Izv., 1:1 (1967), 81–94

Citation in format AMSBIB
\Bibitem{Leo67}
\by A.~F.~Leont'ev
\paper Summability of the Dirichlet series with real exponents for an arbitrary analytic function
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1967
\vol 31
\issue 1
\pages 87--102
\mathnet{http://mi.mathnet.ru/izv2530}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=206221}
\zmath{https://zbmath.org/?q=an:0176.02004|0182.09503}
\transl
\jour Math. USSR-Izv.
\yr 1967
\vol 1
\issue 1
\pages 81--94
\crossref{https://doi.org/10.1070/IM1967v001n01ABEH000548}


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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. A. F. Leont'ev, “Representation of functions by generalized Dirichlet series”, Russian Math. Surveys, 24:2 (1969), 101–178  mathnet  crossref  mathscinet  zmath
    2. A. F. Leont'ev, “Recovery of a function from its coefficients in a Dirichlet series”, Math. USSR-Izv., 5:1 (1971), 131–159  mathnet  crossref  mathscinet  zmath
    3. V. S. Vladimirov, S. M. Nikol'skii, Yu. N. Frolov, “Aleksei Fedorovich Leont'ev (on his sixtieth birthday)”, Russian Math. Surveys, 32:3 (1977), 131–144  mathnet  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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