Pointwise approximation on the Alice Roth’s Swiss cheese

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2025年2月9日

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Eduardo S. Zeron,
Jesús Emmanuel Castillo

摘要

We show that the complex conjugate function $z\mapsto \overline{z}$ $z \mapsto \bar{z}$ cannot be pointwise approximated by holomorphic polynomials on the Alice Roth’s Swiss cheese $Q_R\subset \mathbb {C}$ $Q_{R} \subset C$ . Moreover, under some extra hypotheses, we also show that the complex conjugate cannot be pointwise approximated either by functions holomorphic on $Q_R$ $Q_{R}$ .