Inner factors of Dirichlet space functions
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911328146292736 |
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| author | Hartz, Michael Richter, Stefan |
| author_facet | Hartz, Michael Richter, Stefan |
| contents | Every function in the Dirichlet space on the unit disc has an inner/outer factorization. We study which inner functions occur in this way. For Blaschke products, this is the well known question of which subsets of the disc are zero sets for the Dirichlet space. We also consider singular inner factors, and in particular prove an analogue of the Shapiro-Shields theorem in this setting. Our results on singular inner factors also yield new sufficient conditions for zero sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17723 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inner factors of Dirichlet space functions Hartz, Michael Richter, Stefan Complex Variables Functional Analysis Primary 30J05, Secondary 30H25, 46E22 Every function in the Dirichlet space on the unit disc has an inner/outer factorization. We study which inner functions occur in this way. For Blaschke products, this is the well known question of which subsets of the disc are zero sets for the Dirichlet space. We also consider singular inner factors, and in particular prove an analogue of the Shapiro-Shields theorem in this setting. Our results on singular inner factors also yield new sufficient conditions for zero sets. |
| title | Inner factors of Dirichlet space functions |
| topic | Complex Variables Functional Analysis Primary 30J05, Secondary 30H25, 46E22 |
| url | https://arxiv.org/abs/2512.17723 |