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Article Dans Une Revue Publicacions Matemàtiques. Année : 2014

On separated Carleson sequences in the unit disc of ${\mathbb{C}}.$

Eric Amar

Résumé

The interpolating sequences for $H^{\infty }({\mathbb{D}}),$ the bounded holomorphic function in the unit disc ${\mathbb{D}}$ of the complex plane ${\mathbb{C}},$ {\small where characterised by L. Carleson by metric conditions on the points. They are also characterised by "dual boundedness" conditions which imply an infinity of functions. A. Hartmann proved recently that just one function in $H^{\infty }({\mathbb{D}})$ was enough to characterize interpolating sequences for $H^{\infty }({\mathbb{D}}).$ In this work we use the "hard" part of the proof of Carleson for the Corona theorem, to extend Hartman's result and answer a question he asked in his paper.}\ \par
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Dates et versions

hal-00624583 , version 1 (19-09-2011)
hal-00624583 , version 2 (18-09-2012)

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Citer

Eric Amar. On separated Carleson sequences in the unit disc of ${\mathbb{C}}.$. Publicacions Matemàtiques., 2014, 58 (2), pp.401-414. ⟨hal-00624583v2⟩

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