We consider Mergelyan sets and Farrell sets for \(H^p\)\((1\le p < \infty )\) spaces in the unit disc for both the weak topology and the norm topology, and give a short proof of a theorem of Pérez-González which answers a question proposed by Rubel and Stray (J Approx Theory 37:44–50, 1983).
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The author is grateful to the referee for careful reading of the manuscript and corrections.
Funding was provided by Simons Foundation (US) (Grant No. 430329).
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Danielyan, A.A. On a joint approximation question in \(H^p\) spaces. Arch. Math. (2020). https://doi.org/10.1007/s00013-020-01478-9
- Mergelyan set
- Farrell set
- \(H^p\) spaces
- Joint approximation by polynomials
Mathematics Subject Classification
- Primary 30E10