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Ufimsk. Mat. Zh., 2013, Volume 5, Issue 3, Pages 96–120 (Mi ufa212)  

This article is cited in 9 scientific papers (total in 9 papers)

A closedness of set of Dirichlet series sums

A. S. Krivosheyeva, O. A. Krivosheyevab

a Institute of Mathematics USC RAS, Chernyshevsky str., 112, 450008, Ufa, Russia
b Bashkir State University, Z. Validi str., 32, 450074, Ufa, Russia

Abstract: In the work we consider Dirichlet series. We study the problem of closedness for the set of the sums for such series in the space of functions holomorphic in a convex domain of a complex plane with a topology of uniform convergence on compact subsets. We obtain necessary and sufficient conditions under those every function from the closure of a linear span of exponents with positive indices is represented by a Dirichlet series. These conditions can be formulated only in terms of geometric characteristics of an index sequence and of the convex domain.

Keywords: exponent, convex domain, Dirichlet series, entire function, invariant subspace.

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English version:
Ufa Mathematical Journal, 2013, 5:3, 94–117 (PDF, 296 kB);

UDC: 517.5
MSC: 41A05, 41А30
Received: 28.05.2013

Citation: A. S. Krivosheyev, O. A. Krivosheyeva, “A closedness of set of Dirichlet series sums”, Ufimsk. Mat. Zh., 5:3 (2013), 96–120; Ufa Math. J., 5:3 (2013), 94–117

Citation in format AMSBIB
\by A.~S.~Krivosheyev, O.~A.~Krivosheyeva
\paper A closedness of set of Dirichlet series sums
\jour Ufimsk. Mat. Zh.
\yr 2013
\vol 5
\issue 3
\pages 96--120
\jour Ufa Math. J.
\yr 2013
\vol 5
\issue 3
\pages 94--117

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    This publication is cited in the following articles:
    1. A. I. Abdulnagimov, A. S. Krivoshyev, “Properly distributed subsequence on the line”, Ufa Math. J., 7:1 (2015), 3–12  mathnet  crossref  mathscinet  isi  elib
    2. S. G. Merzlyakov, S. V. Popenov, “Interpolation by series of exponentials in $H(D)$ with real nodes”, Ufa Math. J., 7:1 (2015), 46–57  mathnet  crossref  isi  elib
    3. A. I. Abdulnagimov, A. S. Krivosheyev, “Properly distributed subsets in complex plane”, St. Petersburg Math. J., 28:4 (2017), 433–464  mathnet  crossref  mathscinet  isi  elib
    4. A. I. Abdulnagimov, A. S. Krivoshyev, “Representation of analytic functions”, Ufa Math. J., 8:4 (2016), 3–23  mathnet  crossref  mathscinet  isi  elib
    5. O. A. Krivosheyeva, A. S. Krivosheyev, “A representation of functions from an invariant subspace with almost real spectrum”, St. Petersburg Math. J., 29:4 (2018), 603–641  mathnet  crossref  mathscinet  isi  elib
    6. A. S. Krivosheev, A. F. Kuzhaev, “On one Leontiev-Levin theorem”, Ufa Math. J., 9:3 (2017), 87–99  mathnet  crossref  isi  elib
    7. O. A. Krivosheeva, “Basis in invariant subspace of analytical functions”, Ufa Math. J., 10:2 (2018), 58–77  mathnet  crossref  isi
    8. O. A. Krivosheeva, A. S. Krivosheev, “Singular points for the sum of a series of exponential monomials”, Probl. anal. Issues Anal., 7(25), spetsvypusk (2018), 72–87  mathnet  crossref  elib
    9. S. G. Merzlyakov, S. V. Popenov, “Interpolyatsiya summami ryadov eksponent s pokazatelyami, sguschayuschimisya v odnom napravlenii”, Kompleksnyi analiz. Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 162, VINITI RAN, M., 2019, 62–79  mathnet  mathscinet
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