Extensions of the disc algebra and of Mergelyanʼs theorem

Iakovos Androulidakis; Vassili Nestoridis

doi:10.1016/j.crma.2011.06.002

Complex Analysis/Harmonic Analysis

Extensions of the disc algebra and of Mergelyanʼs theorem
[Extensions de lʼalgèbre du disque et du théorème de Mergelyan]

Présenté par : Jean-Pierre Kahane

Iakovos Androulidakis ¹ ; Vassili Nestoridis ²

¹ Georg-August Universität Göttingen, Institute of Mathematics, Bunsenstrasse 3-5, 37073 Göttingen, Germany
² Department of Mathematics, Panepistemiopolis, 157-84, Athens, Greece

Comptes Rendus. Mathématique, Volume 349 (2011) no. 13-14, pp. 745-748.

Résumé
Abstract

A toute compactification métrisable S du plan complexe, nous associons une extension $A (D, S)$ de lʼ algèbre du disque $A (D)$ . Un cas fondamental est celui où $S = C \cup {\infty}$ . Nous déterminons lʼ ensemble de limites uniformes des polynômes sur le disque unité fermé $\bar{D}$ , par rapport à la métrique chordale ; ensuite nous étendons cette étude au cas géneral.

We investigate the uniform limits of the set of polynomials on the closed unit disc $\bar{D}$ with respect to the chordal metric χ. More generally, we examine analogous questions replacing $C \cup {\infty}$ by other metrizable compactifications of $C$ .

Reçu le : 2011-04-28
Accepté le : 2011-06-01
Publié le : 2011-06-17

DOI : 10.1016/j.crma.2011.06.002

Affiliations des auteurs :

Iakovos Androulidakis ¹ ; Vassili Nestoridis ²

¹ Georg-August Universität Göttingen, Institute of Mathematics, Bunsenstrasse 3-5, 37073 Göttingen, Germany
² Department of Mathematics, Panepistemiopolis, 157-84, Athens, Greece

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     author = {Iakovos Androulidakis and Vassili Nestoridis},
     title = {Extensions of the disc algebra and of {Mergelyan's} theorem},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {745--748},
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     volume = {349},
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     year = {2011},
     doi = {10.1016/j.crma.2011.06.002},
     language = {en},
}

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Iakovos Androulidakis; Vassili Nestoridis. Extensions of the disc algebra and of Mergelyanʼs theorem. Comptes Rendus. Mathématique, Volume 349 (2011) no. 13-14, pp. 745-748. doi : 10.1016/j.crma.2011.06.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.06.002/

Bibliographie
Cité par

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[7] V. Nestoridis An extension of the disc algebra, 2010 | arXiv

[8] V. Nestoridis, An extension of the disc algebra, I, 2010, submitted for publication.

[9] V. Nestoridis; N. Papadatos Another extension of the disc algebra, 2010 | arXiv

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[11] V. Nestoridis; I. Papadoperakis A remark on two extensions of the disc algebra and Mergelyanʼs theorem | arXiv

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