Carleman approximation by non-critical functions on Riemann surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917150023745536 |
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| author | Učakar, Beno |
| author_facet | Učakar, Beno |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Carleman approximation by non-critical functions on Riemann surfaces Učakar, Beno Complex Variables 30E10 (Primary) 30D20, 58K05 (Secondary) 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. |
| title | Carleman approximation by non-critical functions on Riemann surfaces |
| topic | Complex Variables 30E10 (Primary) 30D20, 58K05 (Secondary) |
| url | https://arxiv.org/abs/2508.05765 |