Abstract
After having defined the Koenigs function of a semigroup in the previous chapter, now we turn our attention to the second characteristic feature of a semigroup: the infinitesimal generator. We see how to relate semigroups to Cauchy problems, showing that every semigroup is completely determined by a holomorphic vector field in the unit disc, its infinitesimal generator. Once shown the existence of such a vector field, we will focus on different descriptions and characterizations of infinitesimal generators and discuss several of their properties and examples.
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Bracci, F., Contreras, M.D., Díaz-Madrigal, S. (2020). Infinitesimal Generators. In: Continuous Semigroups of Holomorphic Self-maps of the Unit Disc. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-36782-4_10
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DOI: https://doi.org/10.1007/978-3-030-36782-4_10
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-36781-7
Online ISBN: 978-3-030-36782-4
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