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2014 On separated Carleson sequences in the unit disc
Eric Amar
Publ. Mat. 58(2): 401-414 (2014).


The interpolating sequences $S$ for $H^{\infty }(\mathbb{D})$, the bounded holomorphic functions in the unit disc $\mathbb{D}$ of the complex plane $\mathbb{C}$, were characterized by L. Carleson using metric conditions on $S$. Alternatively, to characterize interpolating sequences we can use the existence in $H^{\infty }(\mathbb{D})$ of an infinity of functions $\lbrace \rho _{a}\rbrace _{a\in S}$, uniformly bounded in $\mathbb{D}$, the function $\rho _{a}$ being $1$ at the point $a\in S$ and $0$ at any $b\in S\setminus \lbrace a\rbrace$. A. Hartmann recently proved 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 Carleson's proof of the corona theorem to extend Hartmann's result and to answer a question he asked in his paper.


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Eric Amar. "On separated Carleson sequences in the unit disc." Publ. Mat. 58 (2) 401 - 414, 2014.


Published: 2014
First available in Project Euclid: 21 July 2014

zbMATH: 1304.62082
MathSciNet: MR3264504

Primary: 30H10 , 30H80

Keywords: Carleson measures , Interpolating sequences

Rights: Copyright © 2014 Universitat Autònoma de Barcelona, Departament de Matemàtiques


Vol.58 • No. 2 • 2014
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