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

Author
A. F. Grishin, N. V. Quynh
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.43.1.94-99
Reference
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2. Azarin V.S. On the asymptotic behavior of subharmonic functions of finite order// Mat. Sb. 1979. V.108, 2. P. 147167. (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. 1024. (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
Volume
43
Issue
1
Year
2015
Journal
Matematychni Studii
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