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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.20603 |
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| _version_ | 1866914286640562176 |
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| author | Dovbush, Peter V Krantz, Steven G |
| author_facet | Dovbush, Peter V Krantz, Steven G |
| contents | We characterize normal families in the unit ball as those families of analytic functions whose restrictions to each complex line through the origin are normal. We then generalize this result to a characterization of normal functions according to behavior on analytic discs. A simple proof of an old theorem of Hartog's that a formal power series at 0 in $\Cn$ is convergent if its restriction to each complex line through the origin is convergent are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20603 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Canonical Characterization of Normal Functions Dovbush, Peter V Krantz, Steven G Complex Variables 32A18 We characterize normal families in the unit ball as those families of analytic functions whose restrictions to each complex line through the origin are normal. We then generalize this result to a characterization of normal functions according to behavior on analytic discs. A simple proof of an old theorem of Hartog's that a formal power series at 0 in $\Cn$ is convergent if its restriction to each complex line through the origin is convergent are given. |
| title | A Canonical Characterization of Normal Functions |
| topic | Complex Variables 32A18 |
| url | https://arxiv.org/abs/2601.20603 |