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Composition operators and a pull-back measure formula

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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 fuctions 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 functionsf belonging to the Nevanlinna class which are solutions of the functional equationf ° π=λf, for some constant λ), thus generalizing earlier results obtained by R. Mortini and this author.

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Authors and Affiliations

  1. Department of Mathematics, University of Nebraska, 68182-0243, Omaha, NE

    Valentin Matache

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  1. Valentin Matache
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Matache, V. Composition operators and a pull-back measure formula. Integr equ oper theory 39, 329–334 (2001). https://doi.org/10.1007/BF01332660

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  • DOI: https://doi.org/10.1007/BF01332660

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