### Abstract

A pull-back measure formula obtained in some particular cases by E. A. Nordgren and this author is generalized in the framework of boundary measures for zero-free Nevanlinna class functions on the unit polydisk. The formula is used to characterize the zero-free Nevanlinna class functions which are solutions of Schröder's equation induced by a polydisk automorphism φ (i.e. to determine the zero-free functions f belonging to the Nevanlinna class which are solutions of the functional equation f o φ = λf, for some constant λ), thus generalizing earlier results obtained by R. Mortini and this author.

Original language | English (US) |
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Pages (from-to) | 329-334 |

Number of pages | 6 |

Journal | Integral Equations and Operator Theory |

Volume | 39 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 1 2001 |

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### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory