
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 $u_1u_2$ 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
$$
\sum_{R/2\lez_j\le R}r_j=o(R^{\gamma+1}),\qquad R\to\infty.
$$
Asymptotics of the difference of associated measures is characterized by the behavior of the function
$$
\max_{R\lez/2}\int_0^R\frac{\mu_1(z,t)\mu_2(z,t)}t dt
$$
at infinity.
Keywords:
subharmonic functions, associated measure, Jensen formula, harmonic functions, Riesz representation.
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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 83107
\mathnet{http://mi.mathnet.ru/ufa65}
\zmath{https://zbmath.org/?q=an:1240.31002}
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