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Interpolating by Functions from Model Subspaces in $$H^1$$H1

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Given an interpolating Blaschke product B with zeros $$\{a_j\}$${aj}, we seek to characterize the sequences of values $$\{w_j\}$${wj} for which the interpolation problem $$\begin{aligned} f(a_j)=w_j\qquad (j=1,2,\dots ) \end{aligned}$$f(aj)=wj(j=1,2,⋯)can be solved… Click to show full abstract

Given an interpolating Blaschke product B with zeros $$\{a_j\}$${aj}, we seek to characterize the sequences of values $$\{w_j\}$${wj} for which the interpolation problem $$\begin{aligned} f(a_j)=w_j\qquad (j=1,2,\dots ) \end{aligned}$$f(aj)=wj(j=1,2,⋯)can be solved with a function f from the model subspace $$H^1\cap B\overline{H^1_0}$$H1∩BH01¯ of the Hardy space $$H^1$$H1.

Keywords: model subspaces; model; functions model; interpolating functions

Journal Title: Integral Equations and Operator Theory
Year Published: 2018

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