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Matematicheskaya Fizika, Analiz, Geometriya [Mathematical Physics, Analysis, Geometry], 2005, Volume 12, Number 1, Pages 25–72
(Mi jmag171)
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This article is cited in 6 scientific papers (total in 6 papers)
New formulas for inidicators of subharmonic functions
A. F. Grishinab, T. I. Malyutinac a B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov
b V. N. Karazin Kharkiv National University, Faculty of Mathematics and Mechanics
c Ukrainian Academy of Banking
Abstract:
The paper concerns the theory of growth of subharmonic functions of finite order. Main characteristics of growth of ones are indicator and lower indicator. There is a theorem among main results of the paper where new formulas for indicator are showed. A criterium of complete regularity in sense of Levin and Pfluger is demonstrated as application. This criterium is formulated for a fixed ray. It is sharpening of a theorem of B. Ya. Levin. Another theorems attributed to the main results is in-deps elaboration of a theorem of Bernstein. Often under investigation of a subharmonic function it is likened to one that produced by translation of Riesz' measure of initial function to a finite system of rays. New property of the operation of translation are among other results of the paper.
Received: 02.09.2004
Citation:
A. F. Grishin, T. I. Malyutina, “New formulas for inidicators of subharmonic functions”, Mat. Fiz. Anal. Geom., 12:1 (2005), 25–72
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https://www.mathnet.ru/eng/jmag171 https://www.mathnet.ru/eng/jmag/v12/i1/p25
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