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Interpolating by Functions from Model Subspaces in \(H^1\)

Open Problems
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Abstract

Given an interpolating Blaschke product B with zeros \(\{a_j\}\), we seek to characterize the sequences of values \(\{w_j\}\) for which the interpolation problem
$$\begin{aligned} f(a_j)=w_j\qquad (j=1,2,\dots ) \end{aligned}$$
can be solved with a function f from the model subspace \(H^1\cap B\overline{H^1_0}\) of the Hardy space \(H^1\).

Keywords

Inner function Interpolating Blaschke product Hardy spaces Model subspaces 

Mathematics Subject Classification

30H05 30H10 30J05 47B35 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departament de Matemàtiques i Informàtica, IMUB and BGSMathUniversitat de BarcelonaBarcelonaSpain
  2. 2.Institució Catalana de Recerca i Estudis Avançats (ICREA)BarcelonaSpain

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