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On weighted compositions preserving the Carathéodory class

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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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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    Irina Arévalo & Dragan Vukotić

  2. Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar, Chile

    Rodrigo Hernández

  3. Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, 80101, Joensuu, Finland

    María J. Martín

Authors
  1. Irina Arévalo
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  2. Rodrigo Hernández
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  3. María J. Martín
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  4. Dragan Vukotić
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Corresponding author

Correspondence to Dragan Vukotić.

Additional information

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

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