Comptes Rendus
Mathematical Analysis
Abstract theory of universal series and an application to Dirichlet series
Comptes Rendus. Mathématique, Volume 341 (2005) no. 9, pp. 539-543.

We present an abstract theory of universal series; in particular, we give a necessary and sufficient condition for the existence of universal series of a certain type. Most of the known results can be proved or strengthened by using this condition. We also obtain new results, for example, related to universal Dirichlet series.

Ainsi nous obtenons des démonstrations simples et des versions améliorées de la plupart de résultats connus. Nous obtenons aussi des résultats nouveaux, par example dans le cas de séries de Dirichlet.

Published online:
DOI: 10.1016/j.crma.2005.09.028

Vassili Nestoridis 1; Chris Papadimitropoulos 1

1 Department of Mathematics, Panepistimiopolis, University of Athens, Athens, 15784, Greece
     author = {Vassili Nestoridis and Chris Papadimitropoulos},
     title = {Abstract theory of universal series and an application to {Dirichlet} series},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {539--543},
     publisher = {Elsevier},
     volume = {341},
     number = {9},
     year = {2005},
     doi = {10.1016/j.crma.2005.09.028},
     language = {en},
AU  - Vassili Nestoridis
AU  - Chris Papadimitropoulos
TI  - Abstract theory of universal series and an application to Dirichlet series
JO  - Comptes Rendus. Mathématique
PY  - 2005
SP  - 539
EP  - 543
VL  - 341
IS  - 9
PB  - Elsevier
DO  - 10.1016/j.crma.2005.09.028
LA  - en
ID  - CRMATH_2005__341_9_539_0
ER  - 
%0 Journal Article
%A Vassili Nestoridis
%A Chris Papadimitropoulos
%T Abstract theory of universal series and an application to Dirichlet series
%J Comptes Rendus. Mathématique
%D 2005
%P 539-543
%V 341
%N 9
%I Elsevier
%R 10.1016/j.crma.2005.09.028
%G en
%F CRMATH_2005__341_9_539_0
Vassili Nestoridis; Chris Papadimitropoulos. Abstract theory of universal series and an application to Dirichlet series. Comptes Rendus. Mathématique, Volume 341 (2005) no. 9, pp. 539-543. doi : 10.1016/j.crma.2005.09.028.

[1] D. Armitage Universal overconvergence of polynomial expansions of harmonic functions, J. Approx. Theory, Volume 118 (2002) no. 2, pp. 225-234

[2] B. Bagchi A joint universality theorem for Dirichlet L-functions, Math. Z., Volume 181 (1982), pp. 319-334

[3] F. Bayart Topological and algebraic genericity of divergence and universality, Studia Math., Volume 167 (2005) no. 2

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

[5] G. Costakis, V. Nestoridis, I. Papadoperakis, Universal Laurent series, submitted for publication

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

[7] J.-P. Kahane Baire's category theorem and trigonometric series, J. Anal. Math., Volume 80 (2000), pp. 1-37

[8] J.-P. Kahane; V. Nestoridis Séries de Taylor et séries trigonométriques universelles au sens de Menchoff, J. Math. Pures Appl. (9), Volume 79 (2000) no. 9, pp. 855-862

[9] Ch. Kariofillis, Ch. Konstadilaki, V. Nestoridis, Smooth universal Taylor series, submitted for publication

[10] E. Katsoprinakis; V. Nestoridis; I. Papadoperakis Universal Faber series, Analysis, Volume 21 (2001), pp. 339-363

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

[12] W. Luh Universal approximation properties of overconvergent power series on open sets, Analysis, Volume 6 (1986), pp. 191-207

[13] A. Melas; V. Nestoridis Universality of Taylor series as a generic property of holomorphic functions, Adv. Math., Volume 157 (2001), pp. 138-176

[14] A. Melas; V. Nestoridis On various types of universal Taylor series, Complex Variables, Volume 44 (2001), pp. 245-258

[15] D. Menchoff, Sur les séries trigonometriques universelles, C. R. Acad. Sci. URSS 49 (2) 1293–1306

[16] V. Nestoridis Universal Taylor series, Ann. Inst. Fourier, Volume 46 (1996), pp. 1293-1306

[17] V. Nestoridis A strong notion of universal Taylor series, J. London Math. Soc. (2), Volume 68 (2003), pp. 712-724

[18] A.I. Seleznev Sur les séries de puissances universelles, Mat. Sbornik (N.S.), Volume 28 (1951), pp. 453-460

[19] L. Tomm; R. Trautner A universal power series for approximation of measurable functions, Analysis, Volume 2 (1982), pp. 1-6

[20] V. Vlachou On some classes of universal functions, Analysis, Volume 22 (2002), pp. 149-161

Cited by Sources:

Research supported by the program “EΠEAEK II, ΠYΘAΓOPAΣ II” (75% European grant and 25% Greek national grant).

Comments - Policy