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Density of certain polynomial modules. (English) Zbl 1354.30024
Let \(X\) be a compact subset of the complex plane \({\mathbb C}\). The authors of the paper under review for a given positive integer \(d\) study the problem of density of the set of functions of the form \(p+\bar z^dq\), where \(p\) and \(q\) are polynomials in the space \(C(X)\) of continuous functions on \(X\). In concoction with this problem they study the problem of taking roots in model spaces, i.e., subspaces of \(H^2\) that are invariant under backward shift.

MSC:
30E10 Approximation in the complex plane
30H10 Hardy spaces
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