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ЖУРНАЛЫ // Журнал математической физики, анализа, геометрии // Архив

Матем. физ., анал., геом., 2002, том 9, номер 2, страницы 146–167 (Mi jmag279)

Эта публикация цитируется в 6 статьях

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

Аннотация: 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.

MSC: Primary 32A20; Secondary 32A22, 30D30, 30D20, 30D35

Поступила в редакцию: 06.09.2001

Язык публикации: английский



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