Abstract
Let \((\phi _t)\) be a semigroup of holomorphic self-maps of \(\mathbb {D}\). In this note, we use an abstract approach to define the Koenigs function of \((\phi _t)\) and “holomorphic models” and show how to deduce the existence and properties of the infinitesimal generator of \((\phi _t)\) from this construction.
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In Memory of our beloved friend Sasha Vasil’ev.
F. Bracci: Partially supported by the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006. M. D. Contreras and S. Díaz-Madrigal: Partially supported by the Ministerio de Economía y Competitividad and the European Union (FEDER), Project MTM2015-63699-P, and by La Consejería de Economía y Competitividad de la Junta de Andalucía.
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Bracci, F., Contreras, M.D. & Díaz-Madrigal, S. On the Koenigs function of semigroups of holomorphic self-maps of the unit disc. Anal.Math.Phys. 8, 521–540 (2018). https://doi.org/10.1007/s13324-018-0254-4
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DOI: https://doi.org/10.1007/s13324-018-0254-4