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Soit un domaine plan ; y a-t-il des suites telles que toute suite bornée puisse être interpolée en par une fonction régulière et bornée dans ? Dans l’affirmative est-il vrai que toute suite qui tend assez rapidement vers la frontière de possède cette propriété ? On répond affirmativement à ces deux questions dans le cas où est le cercle-unité.
Recently in this Journal J. Esterlé gave a new proof of the Wiener Tauberian theorem for using the Ahlfors-Heins theorem for bounded analytic functions on a half-plane. We here use essentially the same method to prove the analogous result for Beurling algebras . Our estimates need a theorem of Hayman and Korenblum.
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