| Title:
|
Asymptotic stability for sets of polynomials (English) |
| Author:
|
Müller, Thomas W. |
| Author:
|
Schlage-Puchta, Jan-Christoph |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
151-155 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce the concept of asymptotic stability for a set of complex functions analytic around the origin, implicitly contained in an earlier paper of the first mentioned author (“Finite group actions and asymptotic expansion of $e^{P(z)}$", Combinatorica 17 (1997), 523 – 554). As a consequence of our main result we find that the collection of entire functions $\exp (\mathfrak {P})$ with $\mathfrak {P}$ the set of all real polynomials $P(z)$ satisfying Hayman’s condition $[z^n]\exp (P(z))>0\,(n\ge n_0)$ is asymptotically stable. This answers a question raised in loc. cit. (English) |
| Keyword:
|
power series |
| Keyword:
|
coefficients |
| Keyword:
|
asymptotic expansion |
| MSC:
|
30B10 |
| MSC:
|
30D15 |
| idZBL:
|
Zbl 1109.30001 |
| idMR:
|
MR2164664 |
| . |
| Date available:
|
2008-06-06T22:45:35Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107945 |
| . |
| Reference:
|
[1] Dress A., Müller T.: Decomposable functors and the exponential principle.Adv. in Math. 129 (1997), 188–221. Zbl 0947.05002, MR 1462733 |
| Reference:
|
[2] Hayman W.: A generalisation of Stirling’s formula.J. Reine u. Angew. Math. 196 (1956), 67–95. MR 0080749 |
| Reference:
|
[3] Müller T.: Finite group actions and asymptotic expansion of $e^{P(z)}$.Combinatorica 17 (1997), 523–554. MR 1645690 |
| Reference:
|
[4] Stanley R. P.: Enumerative Combinatorics.vol. 2, Cambridge University Press, 1999. Zbl 0945.05006, MR 1676282 |
| . |
