| Title:
|
Further remarks on formal power series (English) |
| Author:
|
Borkowski, Marcin |
| Author:
|
Maćkowiak, Piotr |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
549-555 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
formal power series |
| Keyword:
|
superposition |
| Keyword:
|
boundary convergence |
| MSC:
|
13F25 |
| MSC:
|
13J05 |
| idMR:
|
MR3016425 |
| . |
| Date available:
|
2013-03-02T13:38:51Z |
| Last updated:
|
2015-02-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143189 |
| . |
| Reference:
|
[1] Bugajewski D., Gan X.-X.: A note on formal power series.Comment. Math. Univ. Carolin. 51 (2010), no. 4, 595–604. Zbl 1224.13025, MR 2858263 |
| Reference:
|
[2] Bugajewski D., Gan X.-X.: On formal Laurent series.Bull. Braz. Math. Soc., New Series 42 (2011), no. 3, 415–437. MR 2833811, 10.1007/s00574-011-0023-6 |
| Reference:
|
[3] Gan X.-X., Knox N.: On composition of formal power series.Int. J. Math. Math. Sci. 30 (2002), no. 12, 761–770. Zbl 0998.13010, MR 1917671, 10.1155/S0161171202107150 |
| Reference:
|
[4] Herzog F., Piranian, G.: Sets of convergence of Taylor series I.Duke Math. J. 16 (1949), 529–534. Zbl 0034.04806, MR 0031049, 10.1215/S0012-7094-49-01647-6 |
| Reference:
|
[5] Lang S.: Complex Analysis.Springer, 4th edition, New York, 1999. Zbl 0933.30001, MR 1659317 |
| . |
