Non-analytic sets and \(QC\)-level sets in the maximal ideal space of \(H^\infty\). (English) Zbl 1267.30105
The authors investigate the properties and their relations of two interesting classes of subsets of the maximal ideal space of \(H^\infty\): these are the \(QC\)-level sets and the “non-analytic sets”
\[
N(f)=\overline{\bigcup_{x\in X} \text{supp \(\mu_x\)}},
\]
where \(f\in L^\infty\) and \(X=\big\{x\in M(H^\infty): f|_{\text{supp }\mu_x}\)
Reviewer: Raymond Mortini (Metz)
MSC:
| 30H05 | Spaces of bounded analytic functions of one complex variable |
| 46J15 | Banach algebras of differentiable or analytic functions, \(H^p\)-spaces |
| 46J20 | Ideals, maximal ideals, boundaries |
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