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Interpolation by bounded functions

W. K. Hayman — 1958

Annales de l'institut Fourier

Soit D un domaine plan ; y a-t-il des suites z n telles que toute suite bornée w puisse être interpolée en z n par une fonction f ( z ) régulière et bornée dans D  ? Dans l’affirmative est-il vrai que toute suite z n qui tend assez rapidement vers la frontière de D possède cette propriété ? On répond affirmativement à ces deux questions dans le cas où D est le cercle-unité.

Esterlè's proof of the tauberian theorem for Beurling algebras

H. G. DalesW. K. Hayman — 1981

Annales de l'institut Fourier

Recently in this Journal J. Esterlé gave a new proof of the Wiener Tauberian theorem for L 1 ( R ) 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 L φ 1 ( R ) . Our estimates need a theorem of Hayman and Korenblum.

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