### 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 | |

State | Published - Mar 1 2001 |

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### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory

### Cite this

**Composition operators and a pull-back measure formula.** / Matache, Valentin.

Research output: Contribution to journal › Article

*Integral Equations and Operator Theory*, vol. 39, no. 3, pp. 329-334. https://doi.org/10.1007/BF01332660

}

TY - JOUR

T1 - Composition operators and a pull-back measure formula

AU - Matache, Valentin

PY - 2001/3/1

Y1 - 2001/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035292573&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035292573&partnerID=8YFLogxK

U2 - 10.1007/BF01332660

DO - 10.1007/BF01332660

M3 - Article

VL - 39

SP - 329

EP - 334

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 3

ER -