Approximation by rational functions in Hardy space
It is known that the set of rational functions generated by \(\{C (\overline\beta z)=(1- \overline\beta z)^{-1}: \beta\in \widetilde {\mathcal L}\}\) is dense in \(A({\mathbf D})\) if \(\widetilde{\mathcal L}\subseteq {\mathbf D}\) satisfies the Hayman-Lyons condition. The author generalizes the same type result for \(\widetilde {\mathcal L}\) which satisfies the weak Hayman-Lyons condition. Here, \(A( {\mathbf D})\) is a disk algebra and \({\mathbf D}\) is an open unit disc. He notes that it is not known whether the weak Hayman-Lyons condition is necessary in this case.
scientific article; zbMATH DE number 1471523
scientific article