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Ufimsk. Mat. Zh., 2010, Volume 2, Issue 3, Pages 83–107 (Mi ufa65)  

This article is cited in 1 scientific paper (total in 1 paper)

Asymptotics of $\delta $-subharmonic functions and their associated measures

A. A. Rumyantseva

Bashkir State University, Ufa, Russia

Abstract: The relationship of asymptotic behavior of the difference of two subharmonic functions $u_1-u_2$ in a neighborhood of infinity and of the difference of their associative measures $\mu_1-\mu_2$ is considered. The asymptotic behavior of difference is considered outside the exceptional sets of “power” smallness, namely, outside the set, which for any $\gamma$ admits covering by the circles $B(z_j,r_j)$, such that
$$ \sum_{R/2\le|z_j|\le R}r_j=o(R^{\gamma+1}),\qquad R\to\infty. $$
Asymptotics of the difference of associated measures is characterized by the behavior of the function
$$ \max_{R\le|z|/2}|\int_0^R\frac{\mu_1(z,t)-\mu_2(z,t)}t dt| $$
at infinity.

Keywords: subharmonic functions, associated measure, Jensen formula, harmonic functions, Riesz representation.

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Bibliographic databases:

Document Type: Article
UDC: 517.5
Received: 20.06.2010

Citation: A. A. Rumyantseva, “Asymptotics of $\delta $-subharmonic functions and their associated measures”, Ufimsk. Mat. Zh., 2:3 (2010), 83–107

Citation in format AMSBIB
\Bibitem{Rum10}
\by A.~A.~Rumyantseva
\paper Asymptotics of $\delta $-subharmonic functions and their associated measures
\jour Ufimsk. Mat. Zh.
\yr 2010
\vol 2
\issue 3
\pages 83--107
\mathnet{http://mi.mathnet.ru/ufa65}
\zmath{https://zbmath.org/?q=an:1240.31002}


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    This publication is cited in the following articles:
    1. A. A. Makhota, “On completeness of exponential systems in convex domain”, Ufa Math. J., 10:1 (2018), 76–79  mathnet  crossref  isi  elib
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