Comptes Rendus
Complex Analysis/Harmonic Analysis
Universal Taylor series on arbitrary planar domains
Comptes Rendus. Mathématique, Volume 347 (2009) no. 7-8, pp. 363-367.

Let ΩC, ΩC be any domain and ζΩ. Let R=dist(ζ,Ωc)(0,+) and C(ζ,R)={zC:|ζz|=R}. We set J(Ω,ζ)=ΩcC(ζ,R). Then there exists fH(Ω), such that the sequence SN(f,ζ)(z)=n=0Nf(n)(ζ)n!(zζ)n, N=0,1, , approximates any polynomial uniformly on each compact set KJ(Ω,ζ) with CK connected. This property of fH(Ω) is topologically and algebraically generic.

Soit ΩC un domaine, avec ΩC. Soient aussi ζΩ, R=dist(ζ,Ωc)(0,+) et C(ζ,R)={zC:|ζz|=R}. On pose J(Ω,ζ)=ΩcC(ζ,R). Alors il existe fH(Ω) telle que la suite SN(f,ζ)(z)=n=0Nf(n)(ζ)n!(zζ)n, N=0,1, , approche tout polynôme uniformément sur tout compact KJ(Ω,ζ) ne séparant pas le plan. Le phénomène est topologiquement et algébriquement générique.

Published online:
DOI: 10.1016/j.crma.2009.02.007

Vassili Nestoridis 1; Christos Papachristodoulos 1

1 Department of Mathematics, Panepistemiopolis, 157-84, Athenes, Greece
     author = {Vassili Nestoridis and Christos Papachristodoulos},
     title = {Universal {Taylor} series on arbitrary planar domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {363--367},
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     year = {2009},
     doi = {10.1016/j.crma.2009.02.007},
     language = {en},
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VL  - 347
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PB  - Elsevier
DO  - 10.1016/j.crma.2009.02.007
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%0 Journal Article
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%A Christos Papachristodoulos
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%J Comptes Rendus. Mathématique
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Vassili Nestoridis; Christos Papachristodoulos. Universal Taylor series on arbitrary planar domains. Comptes Rendus. Mathématique, Volume 347 (2009) no. 7-8, pp. 363-367. doi : 10.1016/j.crma.2009.02.007.

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