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Matematicheskaya Fizika, Analiz, Geometriya [Mathematical Physics, Analysis, Geometry], 2002, Volume 9, Number 2, Pages 146–167
(Mi jmag279)
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This article is cited in 6 scientific papers (total in 6 papers)
The representation of a meromorphic function as the quotient of entire functions and Paley problem in ${\mathbb C}^n$: survey of some results
B. N. Khabibullin Department of Mathematics, Bashkir State University, 32 Frunze Str., Ufa, Bashkortostan, 450074, Russia
Abstract:
The classical representation problem for a meromorphic function $f$ in $\mathbb C^n$, $n\ge 1$, consists in representing $f$ as the quotient $f=g/h$ of two entire functions $g$ and $h$, each with logarithm of modulus majorized by a function as close as possible to the Nevanlinna characteristic. Here we introduce generalizations of the Nevanlinna characteristic and give a short survey of classical and recent results on the representation of a meromorphic function in terms such characteristics. When $f$ has a finite lower order, the Paley problem on best possible estimates of the growth of entire functions $g$ and $h$ in the representations $f=g/h$ will be considered. Also we point out to some unsolved problems in this area.
Received: 06.09.2001
Citation:
B. N. Khabibullin, “The representation of a meromorphic function as the quotient of entire functions and Paley problem in ${\mathbb C}^n$: survey of some results”, Mat. Fiz. Anal. Geom., 9:2 (2002), 146–167
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https://www.mathnet.ru/eng/jmag279 https://www.mathnet.ru/eng/jmag/v9/i2/p146
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