Azarin limit sets for Radon measures. I (in Russian) |
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| Author |
quynhsonla1988@gmail.com
Karazin Kharkiv National University
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| 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.
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| Keywords |
proximate order; subharmonic function; $\delta$-subharmonic function; limit set; Riesz measure
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| DOI |
doi:10.15330/ms.43.1.94-99
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| 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. – Birkhauser-Basel-Boston-Berlin, 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 |
94-99
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| Volume |
43
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| Issue |
1
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| Year |
2015
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| Journal |
Matematychni Studii
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| Full text of paper | |
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