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Another Look at Average Formulas of Nevanlinna Counting Functions of Holomorphic Self-maps of the Unit Disk

Kim, Hong-Oh

  • Received : 2006.08.14
  • Published : 2008.03.31

Abstract

This is an extended version of the paper [K] of the author. The average formulas on the circles and disks around arbitrary points of Nevanlinna counting functions of holomorphic self-maps of the unit disk, given in terms of the boundary values of the selfmaps, are shown to give another characterization of the whole class or a special subclass of inner functions in terms of Nevanlinna counting function in addition to the previous applications to Rudin's orthogonal functions.

Keywords

Nevanlinna counting function;inner function;sub-averaging property;orthogonal function

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Cited by

  1. Nevanlinna counting function and Carleson function of analytic maps vol.351, pp.2, 2011, https://doi.org/10.1007/s00208-010-0596-1
  2. Complete Nevanlinna counting functions of boundary-preserving Nevanlinna functions vol.60, pp.1, 2015, https://doi.org/10.1080/17476933.2014.898275