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 Mat. Zametki: Year: Volume: Issue: Page: Find

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

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

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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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
2. Yu. F. Korobeinik, “Boundary properties of analytic solutions of differential equations of infinite order”, Math. USSR-Sb., 43:3 (1982), 323–345
3. Yu. F. Korobeinik, “Representing systems”, Russian Math. Surveys, 36:1 (1981), 75–137
4. Yu. F. Korobeinik, “On some representing systems in spaces of analytic functions”, Math. USSR-Izv., 23:3 (1984), 487–509
5. Le Khaǐ Khoǐ, Yu. F. Korobeinik, “Representing systems of exponential functions in polycylindrical domains”, Math. USSR-Sb., 50:2 (1985), 439–456
6. S. N. Melikhov, “On expansion of analytic functions in exponential series”, Math. USSR-Izv., 33:2 (1989), 317–329
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
8. A. V. Abanin, “Nontrivial expansions of zero and absolutely representing systems”, Math. Notes, 57:4 (1995), 335–344
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