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Mat. Zametki, 1977, Volume 21, Issue 5, Pages 641–651 (Mi mz7996)  

This article is cited in 8 scientific papers (total in 8 papers)

The representation of regular functions by Dirichlet series

Yu. I. Mel'nik

Mathematics Institute, Academy of Sciences of the Ukrainian SSR

Abstract: It is proved that if a system of exponents has the property that any function regular in a closed convex domain $\overline G$ can be represented in an open domain $G$ by a Dirichlet series, then any function regular only in $G$ can be represented in $G$ by a Dirichlet series with the same system of exponents. A study is made of the representation of functions regular in $\overline G$ by Dirichlet series that converge in $\overline G$.

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English version:
Mathematical Notes, 1977, 21:5, 360–366

Bibliographic databases:

UDC: 517.5
Received: 31.12.1975

Citation: Yu. I. Mel'nik, “The representation of regular functions by Dirichlet series”, Mat. Zametki, 21:5 (1977), 641–651; Math. Notes, 21:5 (1977), 360–366

Citation in format AMSBIB
\Bibitem{Mel77}
\by Yu.~I.~Mel'nik
\paper The representation of regular functions by Dirichlet series
\jour Mat. Zametki
\yr 1977
\vol 21
\issue 5
\pages 641--651
\mathnet{http://mi.mathnet.ru/mz7996}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=457691}
\zmath{https://zbmath.org/?q=an:0399.30019|0356.30016}
\transl
\jour Math. Notes
\yr 1977
\vol 21
\issue 5
\pages 360--366
\crossref{https://doi.org/10.1007/BF01788232}


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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. Yu. F. Korobeinik, “Interpolation problems, nontrivial expansions of zero, and representing systems”, Math. USSR-Izv., 17:2 (1981), 299–337  mathnet  crossref  mathscinet  zmath  isi
    2. Yu. F. Korobeinik, “Boundary properties of analytic solutions of differential equations of infinite order”, Math. USSR-Sb., 43:3 (1982), 323–345  mathnet  crossref  mathscinet  zmath
    3. Yu. F. Korobeinik, “Representing systems”, Russian Math. Surveys, 36:1 (1981), 75–137  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Yu. F. Korobeinik, “On some representing systems in spaces of analytic functions”, Math. USSR-Izv., 23:3 (1984), 487–509  mathnet  crossref  mathscinet  zmath
    5. Le Khaǐ Khoǐ, Yu. F. Korobeinik, “Representing systems of exponential functions in polycylindrical domains”, Math. USSR-Sb., 50:2 (1985), 439–456  mathnet  crossref  mathscinet  zmath
    6. S. N. Melikhov, “On expansion of analytic functions in exponential series”, Math. USSR-Izv., 33:2 (1989), 317–329  mathnet  crossref  mathscinet  zmath
    7. Yu. F. Korobeinik, “Description of the general form of nontrivial expansions of zero in exponentials. Applications”, Math. USSR-Izv., 39:2 (1992), 1013–1032  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. A. V. Abanin, “Nontrivial expansions of zero and absolutely representing systems”, Math. Notes, 57:4 (1995), 335–344  mathnet  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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