Further remarks on formal power series
Marcin Borkowski; Piotr Maćkowiak
Commentationes Mathematicae Universitatis Carolinae (2012)
- Volume: 53, Issue: 4, page 549-555
- ISSN: 0010-2628
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topBorkowski, Marcin, and Maćkowiak, Piotr. "Further remarks on formal power series." Commentationes Mathematicae Universitatis Carolinae 53.4 (2012): 549-555. <http://eudml.org/doc/252507>.
@article{Borkowski2012,
abstract = {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.},
author = {Borkowski, Marcin, Maćkowiak, Piotr},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {formal power series; superposition; boundary convergence; formal power series; superposition; boundary convergence},
language = {eng},
number = {4},
pages = {549-555},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Further remarks on formal power series},
url = {http://eudml.org/doc/252507},
volume = {53},
year = {2012},
}
TY - JOUR
AU - Borkowski, Marcin
AU - Maćkowiak, Piotr
TI - Further remarks on formal power series
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 4
SP - 549
EP - 555
AB - 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.
LA - eng
KW - formal power series; superposition; boundary convergence; formal power series; superposition; boundary convergence
UR - http://eudml.org/doc/252507
ER -
References
top- Bugajewski D., Gan X.-X., A note on formal power series, Comment. Math. Univ. Carolin. 51 (2010), no. 4, 595–604. Zbl1224.13025MR2858263
- Bugajewski D., Gan X.-X., 10.1007/s00574-011-0023-6, Bull. Braz. Math. Soc., New Series 42 (2011), no. 3, 415–437. MR2833811DOI10.1007/s00574-011-0023-6
- Gan X.-X., Knox N., 10.1155/S0161171202107150, Int. J. Math. Math. Sci. 30 (2002), no. 12, 761–770. Zbl0998.13010MR1917671DOI10.1155/S0161171202107150
- Herzog F., Piranian, G., 10.1215/S0012-7094-49-01647-6, Duke Math. J. 16 (1949), 529–534. Zbl0034.04806MR0031049DOI10.1215/S0012-7094-49-01647-6
- Lang S., Complex Analysis, Springer, 4th edition, New York, 1999. Zbl0933.30001MR1659317
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