# A note on formal power series

Xiao-Xiong Gan; Dariusz Bugajewski

Commentationes Mathematicae Universitatis Carolinae (2010)

- Volume: 51, Issue: 4, page 595-604
- ISSN: 0010-2628

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topGan, Xiao-Xiong, and Bugajewski, Dariusz. "A note on formal power series." Commentationes Mathematicae Universitatis Carolinae 51.4 (2010): 595-604. <http://eudml.org/doc/247132>.

@article{Gan2010,

abstract = {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 $\overline\{\mathbb \{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 $\overline\{\mathbb \{X\}\}_g$ into itself or to map $\{\mathbb \{X\}\}_g$ into itself, respectively.},

author = {Gan, Xiao-Xiong, Bugajewski, Dariusz},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {composition; end behavior of convergence of power series; convex and balanced set; formal power series; composition; end behavior; convergence of power series; convex set; balanced set; formal power series},

language = {eng},

number = {4},

pages = {595-604},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A note on formal power series},

url = {http://eudml.org/doc/247132},

volume = {51},

year = {2010},

}

TY - JOUR

AU - Gan, Xiao-Xiong

AU - Bugajewski, Dariusz

TI - A note on formal power series

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2010

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 51

IS - 4

SP - 595

EP - 604

AB - 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 $\overline{\mathbb {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 $\overline{\mathbb {X}}_g$ into itself or to map ${\mathbb {X}}_g$ into itself, respectively.

LA - eng

KW - composition; end behavior of convergence of power series; convex and balanced set; formal power series; composition; end behavior; convergence of power series; convex set; balanced set; formal power series

UR - http://eudml.org/doc/247132

ER -

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