Abstract
We characterize in various ways the weighted composition transformations which preserve the class \(\mathscr {P}\) of normalized analytic functions in the disk with positive real part. We analyze the meaning of the criteria obtained for various special cases of symbols and identify the fixed points of such transformations.
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Communicated by A. Constantin.
Arévalo, Martín, and Vukotić are supported by MTM2015-65792-P from MINECO and FEDER/EU and partially by the Thematic Research Network MTM2015-69323-REDT, MINECO, Spain. Hernández and Martín are supported by FONDECYT 1150284, Chile. Martín is also supported by Academy of Finland Grant 268009.
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Arévalo, I., Hernández, R., Martín, M.J. et al. On weighted compositions preserving the Carathéodory class. Monatsh Math 187, 459–477 (2018). https://doi.org/10.1007/s00605-017-1093-3
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DOI: https://doi.org/10.1007/s00605-017-1093-3
Keywords
- Functions with positive real part (Carathéodory class)
- Weighted composition transformation
- Angular derivative
- Inner functions
- Fixed points