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

2005/02/21 by Bulat N. Khabibullin
Mathematics · #math.CV #msc:32A15 #msc:32A20 #msc:31A05 #msc:31C10

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published as Matematicheskaya fizika, analiz, geometriya (Ukraine), 9 (2002), no.2, P. 146-167 · LaTeX2e

arxiv created 2005/02/21 · arxiv updated 2009/12/01

Abstract

The classical representation problem for a meromorphic function f in Cⁿ, n>=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.

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