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Mat. Sb., 1991, Volume 182, Number 6, Pages 811–827 (Mi msb1325)  

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

A uniqueness theorem for subharmonic functions of finite order

B. N. Khabibullin

Bashkir State University

Abstract: Let $u$ and $v$ be subharmonic functions of finite order on $\mathbf R^m$. The main theorem of this paper shows that, if $u\leqslant v$, the relation “$\leqslant$” is preserved, in a certain sense, for mass distributions $\mu_u$ and $\mu_v$. This result yields new uniqueness theorems for both subharmonic and entire functions on the complex plane. Corollaries include a broad class of sufficient conditions for the completeness of systems $\{e^{\lambda_nz}\}$ of exponential functions in a complex domain $G$. The conditions for completeness are stated entirely in terms of the distribution of the points of the sequence $\{\lambda_n\}$ in the neighborhood of infinity and in terms of the geometric properties (mixed areas) of $G$.

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English version:
Mathematics of the USSR-Sbornik, 1992, 73:1, 195–210

Bibliographic databases:

UDC: 517.574
MSC: 30E10, 31C05, 31C15, 31B05, 32A15, 32A30, 30D15
Received: 20.10.1989

Citation: B. N. Khabibullin, “A uniqueness theorem for subharmonic functions of finite order”, Mat. Sb., 182:6 (1991), 811–827; Math. USSR-Sb., 73:1 (1992), 195–210

Citation in format AMSBIB
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\by B.~N.~Khabibullin
\paper A~uniqueness theorem for subharmonic functions of finite order
\jour Mat. Sb.
\yr 1991
\vol 182
\issue 6
\pages 811--827
\mathnet{http://mi.mathnet.ru/msb1325}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1126154}
\zmath{https://zbmath.org/?q=an:0782.31003|0762.31001}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992SbMat..73..195K}
\transl
\jour Math. USSR-Sb.
\yr 1992
\vol 73
\issue 1
\pages 195--210
\crossref{https://doi.org/10.1070/SM1992v073n01ABEH002541}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992KA53500011}


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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. B. N. Khabibullin, “Completeness of systems of entire functions in spaces of holomorphic functions”, Math. Notes, 66:4 (1999), 495–506  mathnet  crossref  crossref  mathscinet  isi  elib
    2. B. N. Khabibullin, Z. F. Abdullina, A. P. Rozit, “Teorema edinstvennosti i subgarmonicheskie testovye funktsii”, Algebra i analiz, 30:2 (2018), 318–334  mathnet  elib
  • Математический сборник - 1991 Sbornik: Mathematics (from 1967)
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