Azarin limit sets for Radon measures. I (in Russian) 

Author 
quynhsonla1988@gmail.com
Karazin Kharkiv National University

Abstract 
The theory of limit sets of subharmonic functions and measures which is created by Azarin
and is developed in the works of other mathematicians finds applications in the theory of
growth of entire functions, in other areas of mathematics. The Riesz measure of a $\delta$subharmonic
function is a Radon measure. In the paper limit sets of Radon measure are studied. In particular
we present three different criteria for a given set to be the limit set of some Radon measure.

Keywords 
proximate order; subharmonic function; $\delta$subharmonic function; limit set; Riesz measure

DOI 
doi:10.15330/ms.43.1.9499

Reference 
1. Levin B.Ja. Distribution of zeros of entire functions. – Moscow: Tehn. Teor. Lit., 1956. – 632 p. (in
Russian)
2. Azarin V.S. On the asymptotic behavior of subharmonic functions of finite order// Mat. Sb. – 1979. – V.108, ¹2. – P. 147–167. (in Russian) 3. Azarin V.S. Growth theory of subharmonic functions. – BirkhauserBaselBostonBerlin, 2009. – 259 p. 4. Giner V.B. Limit sets of entire and subharmonic functions. – Dissertation. Kharkov, Kh. N. Univ., 1988. (in Russian) 5. Grishin A.F., Malyutina T.I. On proximate order// Complex analysis and mathematical physics, Krasnoyarsk. –1998. – P. 10–24. (in Russian) 6. Bourbaki N. Integration.– Moscow: Nauka, 1977. – 396 p. (in Russian) 7. Nemytskii V.V., Stepanov V.V. Qualitative theory of differential equations. – Moscow, Leningrad: Tehn. Teor. Lit., 1949. – 448 p. (in Russian) 
Pages 
9499

Volume 
43

Issue 
1

Year 
2015

Journal 
Matematychni Studii

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