• DOI:10.1007/BF02391770
• Corpus ID: 120164882

On the characteristic of functions meromorphic in the unit disk and of their integrals

@article{Hayman1964OnTC,
  title={On the characteristic of functions meromorphic in the unit disk and of their integrals},
  author={Walter Kurt Hayman},
  journal={Acta Mathematica},
  year={1964},
  volume={112},
  pages={181-214}
}

• W. Hayman
• Published 1 December 1964
• Philosophy, Mathematics
• Acta Mathematica

n(r, F) as the number of poles in ]z] d r and = f r n(t, F) dt N(r, F) J0 $ Then T(r, F) = re(r, F) + N(r, F) is called the Nevanlinna characteristic function of F(z). The function T(r, F ) i s convex increasing function of log r, so tha t T(1, F) = lim T(r, F) r--~l always exists as a finite or infinite limit. I f T(1, F) is finite we say tha t F(z) has bounded characteristic in ]z] < 1. Examples show tha t F(z) m a y have bounded characteristic in ]z] < 1, even i f / (z) does not.(1) We may take for instance /(z) to be a regular function