Displaying similar documents to “One of the Possible Formal Desribtions of Deducubility”

A note on formal power series

Xiao-Xiong Gan, Dariusz Bugajewski (2010)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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...

Further remarks on formal power series

Marcin Borkowski, Piotr Maćkowiak (2012)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In this paper, we present a considerable simplification of the proof of a theorem by Gan and Knox, stating a sufficient and necessary condition for existence of a composition of two formal power series. Then, we consider the behavior of such series and their (formal) derivatives at the boundary of the convergence circle, obtaining in particular a theorem of Bugajewski and Gan concerning the structure of the set of points where a formal power series is convergent with all its derivatives. ...

Some gap power series in multidimensional setting

Józef Siciak (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

We study extensions of classical theorems on gap power series of a complex variable to the multidimensional case.