| Title:
|
A note on formal power series (English) |
| Author:
|
Gan, Xiao-Xiong |
| Author:
|
Bugajewski, Dariusz |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
595-604 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
composition |
| Keyword:
|
end behavior of convergence of power series |
| Keyword:
|
convex and balanced set |
| Keyword:
|
formal power series |
| MSC:
|
13F25 |
| MSC:
|
40A30 |
| MSC:
|
52A05 |
| idZBL:
|
Zbl 1224.13025 |
| idMR:
|
MR2858263 |
| . |
| Date available:
|
2010-11-30T16:20:42Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140840 |
| . |
| Reference:
|
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