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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.00466 |
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| _version_ | 1866912174701543424 |
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| author | Magnússon, Benedikt Steinar Snorrason, Bergur |
| author_facet | Magnússon, Benedikt Steinar Snorrason, Bergur |
| contents | Using an annular version of the F. and M. Riesz theorem,
we prove a generalization of the Rudin-Carleson theorem for finitely connected bounded domains. That is,
for a continuous function on a closed set in the boundary of measure zero there is a holomorphic function on the
domain continuous to the boundary. Furthermore, this can be done with interpolation at finitely many points in the domain. The proof relies on an annular version of the F. and M. Riesz theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00466 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Rudin-Carleson theorem for multiply connected domains with interpolation Magnússon, Benedikt Steinar Snorrason, Bergur Complex Variables 30H50 Using an annular version of the F. and M. Riesz theorem, we prove a generalization of the Rudin-Carleson theorem for finitely connected bounded domains. That is, for a continuous function on a closed set in the boundary of measure zero there is a holomorphic function on the domain continuous to the boundary. Furthermore, this can be done with interpolation at finitely many points in the domain. The proof relies on an annular version of the F. and M. Riesz theorem. |
| title | A Rudin-Carleson theorem for multiply connected domains with interpolation |
| topic | Complex Variables 30H50 |
| url | https://arxiv.org/abs/2501.00466 |