Carleman approximation by non-critical functions on Riemann surfaces

Beno Učakar

doi:10.1007/s13324-025-01157-4

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arXiv · 2508.05765

Carleman approximation by non-critical functions on Riemann surfaces

Beno Učakar

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Abstract

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.

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BibTeX RIS

Beno Učakar. 2025-08-07. Carleman approximation by non-critical functions on Riemann surfaces. https://doi.org/10.1007/s13324-025-01157-4

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