Extensions of the disc algebra and of Mergelyanʼs theorem

Androulidakis, Iakovos; Nestoridis, Vassili

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

Androulidakis, Iakovos ¹ ; Nestoridis, Vassili 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, Tome 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 :

Androulidakis, Iakovos ¹ ; Nestoridis, Vassili 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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     title = {Extensions of the disc algebra and of {Mergelyan's} theorem},
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Androulidakis, Iakovos; Nestoridis, Vassili. Extensions of the disc algebra and of Mergelyanʼs theorem. Comptes Rendus. Mathématique, Tome 349 (2011) no. 13-14, pp. 745-748. doi : 10.1016/j.crma.2011.06.002. http://www.numdam.org/articles/10.1016/j.crma.2011.06.002/

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