Commuting analytic functions
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- by Carl C. Cowen PDF
- Trans. Amer. Math. Soc. 283 (1984), 685-695 Request permission
Abstract:
Let $f$ and $g$ (not conformal automorphisms of the unit disk) be analytic mappings of the unit disk into itself. We say $f$ and $g$ commute if $f \circ g = g \circ f$. This paper characterizes those functions $g$ that commute with a given function $f$. Several corollaries of this characterization give qualitative information about $g$ given similar information about $f$, and examples are given in each case to show the limitations of the conclusions. Some of the qualitative properties considered are univalence, fixed point sets, and whether two such $g$ must commute with each other.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 283 (1984), 685-695
- MSC: Primary 30D05; Secondary 39B10
- DOI: https://doi.org/10.1090/S0002-9947-1984-0737892-8
- MathSciNet review: 737892