no. 1-2
Mathematical Analysis
Universal p-adic series
[Séries universelles p-adiques]

Présenté par : Jean-Pierre Kahane

Mouze, Augustin1
1 UMR 8524 et École centrale de Lille, cité scientifique, BP 48, 59651 Villeneuve d'Ascq cedex, France
Comptes Rendus. Mathématique, Tome 349 (2011) no. 1-2, pp. 39-42.

On met en évidence l'existence de séries universelles à coefficients p-adiques en généralisant le théorème original de Fekete à Qp.

We establish the analogue of the original Fekete Theorem in the context of p-adic analysis.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.12.006
Mouze, Augustin 1

1 UMR 8524 et École centrale de Lille, cité scientifique, BP 48, 59651 Villeneuve d'Ascq cedex, France 
@article{CRMATH_2011__349_1-2_39_0,
     author = {Mouze, Augustin},
     title = {Universal \protect\emph{p}-adic series},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {39--42},
     publisher = {Elsevier},
     volume = {349},
     number = {1-2},
     year = {2011},
     doi = {10.1016/j.crma.2010.12.006},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.crma.2010.12.006/}
}
TY  - JOUR
AU  - Mouze, Augustin
TI  - Universal p-adic series
JO  - Comptes Rendus. Mathématique
PY  - 2011
SP  - 39
EP  - 42
VL  - 349
IS  - 1-2
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.crma.2010.12.006/
DO  - 10.1016/j.crma.2010.12.006
LA  - en
ID  - CRMATH_2011__349_1-2_39_0
ER  - 
%0 Journal Article
%A Mouze, Augustin
%T Universal p-adic series
%J Comptes Rendus. Mathématique
%D 2011
%P 39-42
%V 349
%N 1-2
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.crma.2010.12.006/
%R 10.1016/j.crma.2010.12.006
%G en
%F CRMATH_2011__349_1-2_39_0
Mouze, Augustin. Universal p-adic series. Comptes Rendus. Mathématique, Tome 349 (2011) no. 1-2, pp. 39-42. doi : 10.1016/j.crma.2010.12.006. http://archive.numdam.org/articles/10.1016/j.crma.2010.12.006/

[1] Araujo, J.; Schikhof, W.H. The Weierstrass–Stone approximation theorem for p-adic Cn-functions, Ann. Math. Blaise Pascal, Volume 1 (1994) no. 1, pp. 61-74

[2] Bayart, F.; Grosse-Erdmann, K.-G.; Nestoridis, V.; Papadimitropoulos, C. Abstract theory of universal series and applications, Proc. Lond. Math. Soc., Volume 96 (2008), pp. 417-463

[3] Chui, C.K.; Parnes, M.N. Approximation by overconvergence of power series, J. Math. Anal. Appl., Volume 36 (1971), pp. 693-696

[4] Gouvêa, F.Q. p-Adic Numbers. An Introduction, Universitext, Springer-Verlag, Berlin, 1997

[5] Grosse-Erdmann, K.-G. Universal families and hypercyclic operators, Bull. Amer. Math. Soc. (N.S.), Volume 36 (1999) no. 3, pp. 345-381

[6] Kahane, J.P. Baire's category theorem and trigonometric series, J. Anal. Math., Volume 80 (2000), pp. 143-182

[7] Kaplansky, I. The Weierstrass theorem in fields with valuations, Proc. Amer. Math. Soc., Volume 1 (1950), pp. 356-357

[8] Nestoridis, V. Universal Taylor series, Ann. Inst. Fourier (Grenoble), Volume 46 (1996) no. 5, pp. 1293-1306

[9] Luh, W. Approximation analytischer Funktionen durch uberkonvergente Potenzreihen und deren Matrix-Transformierten, Mitt. Math. Sem. Giessen, Volume 88 (1970), pp. 1-56

[10] Pál, G. Zwei kleine Bemerkungen, Tohoku Math. J., Volume 6 (1914/15), pp. 42-43

[11] Robert, A.M. A Course in p-Adic Analysis, Graduate Texts in Mathematics, vol. 198, Springer-Verlag, New York, 2000

[12] Seleznev, A.I. On universal power series, Mat. Sb. (N.S.), Volume 28 (1951), pp. 453-460

Cité par Sources :