|
Universality and ultradifferentiable functions: Fekete's theorem
Author(s):
A.
Mouze;
V.
Nestoridis
Journal:
Proc. Amer. Math. Soc.
138
(2010),
3945-3955.
MSC (2010):
Primary 30K05, 41A58, 26E10
Posted:
May 7, 2010
MathSciNet review:
2679616
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
The purpose of this article is to establish extensions of Fekete's Theorem concerning the existence of universal power series of  functions defined by estimates on successive derivatives.
References:
-
- 1.
- F. Bayart, K.-G. Grosse-Erdmann, V. Nestoridis, C. Papadimitropoulos, Abstract theory of universal series and applications, Proc. London Math. Soc. 96 (2008) 417-463. MR 2396846 (2009j:30006)
- 2.
- P. du Bois Reymond, Über die Fourierschen Reihen, Nachr. Kön. Ges. Wiss. Göttingen 21 (1873) 571-582.
- 3.
- E. Borel, Sur quelques points de la théorie des fonctions, Ann. Sci. École Norm. Sup. 12 (1895) 9-55. MR 1508908
- 4.
- C. Chui, M.N. Parnes, Approximation by overconvergence of power series, J. Math. Anal. Appl. 36 (1971) 683-696. MR 0291472 (45:563)
- 5.
- G. Costakis, M. Marias, V. Nestoridis, Universal Taylor series on open subsets of
 , Analysis 26 (2006) 401-409. MR 2313217 (2008b:41026) - 6.
- K.-G. Grosse Erdmann, Holomorphe Monster und universelle Funktionen, Mitt. Math. Sem. Giersen 176 (1987) 1-84. MR 877464 (88i:30060)
- 7.
- K.-G. Grosse Erdmann, Universal families and hypercyclic operators, Bull. Amer. Math. Soc. (N.S.) 36 (1999) no. 3, 345-381. MR 1685272 (2000c:47001)
- 8.
- J.P. Kahane, Baire's category theorem and trigonometric series, J. Anal. Math. 80 (2000) 143-182. MR 1771526 (2001f:42012)
- 9.
- H. Komatsu, Ultradistributions, I. Structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo, Sect. 1A 20 (1973) 25-105. MR 0320743 (47:9277)
- 10.
- W. Luh, Approximation analytischer Funktionen durch uberkonvergente Potenzreihen und deren Matrix-Transformierten, Mitt. Math. Sem. Giessen 88 (1970) 1-56. MR 0280692 (43:6411)
- 11.
- V. Nestoridis, Universal Taylor series, Ann. Inst. Fourier (Grenoble) 46 (1996) no. 5, 1293-1306. MR 1427126 (97k:30001)
- 12.
- V. Nestoridis, C. Papadimitropoulos, Abstract theory of universal series and an application to Dirichlet series, C. R. Math. Acad. Sci. Paris 341 (2005) no. 9, 539-543. MR 2181390 (2006h:11108)
- 13.
- G. Pál, Zwei kleine Bemerkungen, Tokohu Math. J. 6 (1914/15) 42-43.
- 14.
- H.-J. Petzsche, On E. Borel's theorem, Math. Ann. 282 (1988) 299-313. MR 963018 (89m:46076)
- 15.
- A.I. Seleznev, On universal power series, Math. Sbornik N.S. 28 (1951) 453-460. MR 0041928 (13:23e)
- 16.
- N. Tsirivas, Simultaneous approximation by universal series, Math. Nachr., to appear (2010).
- 17.
- H. Whitney, Analytic extensions of differentiable functions defined in closed sets., Trans. Amer. Math. Soc. 36 (1934) no. 1, 63-89. MR 1501735
- 18.
- A. Zygmund,Trigonometric Series, Cambridge University Press (1979).
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2010):
30K05, 41A58, 26E10
Retrieve articles in all Journals with
MSC (2010):
30K05, 41A58, 26E10
Additional Information:
A.
Mouze
Affiliation:
Laboratoire de Mathématiques, UMR 8524, Cité Scientifique, 59650 Villeneuve d'Ascq, France
Address at time of publication:
École Centrale de Lille, Cité Scientifique, 59650 Villeneuve d'Ascq, France
Email:
Augustin.Mouze@math.univ-lillel.fr
V.
Nestoridis
Affiliation:
Department of Mathematics, Panepistimiopilis, University of Athens, Athens, 15784, Greece
Email:
vnestor@math.uoa.gr
DOI:
10.1090/S0002-9939-10-10380-3
PII:
S 0002-9939(10)10380-3
Keywords:
Universal series,
Taylor series,
infinitely differentiable real functions.
Received by editor(s):
June 25, 2009
Received by editor(s) in revised form:
December 27, 2009 and January 12, 2010
Posted:
May 7, 2010
Communicated by:
Nigel J. Kalton
Copyright of article:
Copyright
2010,
American Mathematical Society
|
