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A note on formal power series

Xiao-Xiong GanDariusz Bugajewski — 2010

Commentationes Mathematicae Universitatis Carolinae

In this note we investigate a relationship between the boundary behavior of power series and the composition of formal power series. In particular, we prove that the composition domain of a formal power series g is convex and balanced which implies that the subset 𝕏 ¯ g consisting of formal power series which can be composed by a formal power series g possesses such properties. We also provide a necessary and sufficient condition for the superposition operator T g to map 𝕏 ¯ g into itself or to map 𝕏 g into...

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