Embedding $H^\infty(\D)$ into $L^\infty(\T)$: a proof without non-tangential limits
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917096126939136 |
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| author | Maletzki, Mario P. |
| author_facet | Maletzki, Mario P. |
| contents | The purpose of this note is to show in an accessible and self-contained way the existence of an isometric algebra embedding from $H^\infty(\D)$ into $L^\infty(\T)$, without appealing to Fatou's classical theorem on non-tangential limits of analytic functions, and relying only on results from complex and functional analysis that are typically covered in a standard undergraduate course. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16489 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Embedding $H^\infty(\D)$ into $L^\infty(\T)$: a proof without non-tangential limits Maletzki, Mario P. Functional Analysis The purpose of this note is to show in an accessible and self-contained way the existence of an isometric algebra embedding from $H^\infty(\D)$ into $L^\infty(\T)$, without appealing to Fatou's classical theorem on non-tangential limits of analytic functions, and relying only on results from complex and functional analysis that are typically covered in a standard undergraduate course. |
| title | Embedding $H^\infty(\D)$ into $L^\infty(\T)$: a proof without non-tangential limits |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2511.16489 |