Best approximations for the weighted combination of the Cauchy--Szegö kernel and its derivative in the mean
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909317815336960 |
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| author | Savchuk, Viktor V. Savchuk, Maryna V. |
| author_facet | Savchuk, Viktor V. Savchuk, Maryna V. |
| contents | In this paper, we study an extremal problem concerning best approximation in the Hardy space $H^1$ on the unit disk $\mathbb D$. Specifically, we consider weighted combinations of the Cauchy-Szegö kernel and its derivative, parametrized by an inner function $φ$ and a complex number $λ$, and provide explicit formula of the best approximation $e_{φ,z}(λ)$ by the subspace $H^1_0$. We also describe the extremal functions associated with this approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10833 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Best approximations for the weighted combination of the Cauchy--Szegö kernel and its derivative in the mean Savchuk, Viktor V. Savchuk, Maryna V. Complex Variables In this paper, we study an extremal problem concerning best approximation in the Hardy space $H^1$ on the unit disk $\mathbb D$. Specifically, we consider weighted combinations of the Cauchy-Szegö kernel and its derivative, parametrized by an inner function $φ$ and a complex number $λ$, and provide explicit formula of the best approximation $e_{φ,z}(λ)$ by the subspace $H^1_0$. We also describe the extremal functions associated with this approximation. |
| title | Best approximations for the weighted combination of the Cauchy--Szegö kernel and its derivative in the mean |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2409.10833 |