Infinitesimal Generators
Springer monographs in mathematicsPublished 1 January 2020
Filippo Bracci, Manuel D. Contreras, Santiago Díaz‐Madrigal
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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.
Keywords
Mathematics