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<p>We present the class of semi-admissible subsets of an open Riemann surface on which Carleman approximation by non-critical holomorphic functions is possible. In particular we characterize closed sets with empty interior on which continuous functions can be approximated by non-critical holomorphic ones. We also consider a different approach, which in some cases gives uniform approximation by non-critical holomorphic functions on more general sets than semi-admissible ones.</p>

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Carleman approximation by non-critical functions on Riemann surfaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月2日

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  • Beno Učakar

摘要

We present the class of semi-admissible subsets of an open Riemann surface on which Carleman approximation by non-critical holomorphic functions is possible. In particular we characterize closed sets with empty interior on which continuous functions can be approximated by non-critical holomorphic ones. We also consider a different approach, which in some cases gives uniform approximation by non-critical holomorphic functions on more general sets than semi-admissible ones.