The representation of a meromorphic function as the quotient of entire functions and Paley problem in n: survey of some results


The classical representation problem for a meromorphic function f in ℂn, n³1,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.


Як цитувати

Khabibullin, B. The Representation of a Meromorphic Function As the Quotient of Entire Functions and Paley Problem in n: Survey of Some Results. Мат. физ. анал. геом. 2002, 9, 146-167.





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