Optimal interpolation in Hardy and Bergman spaces: a reproducing kernel Banach space approach
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916525450985472 |
|---|---|
| author | Groenewald, Gilbert J. ter Horst, Sanne Woerdeman, Hugo J. |
| author_facet | Groenewald, Gilbert J. ter Horst, Sanne Woerdeman, Hugo J. |
| contents | After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the setting of Hardy spaces $H^p$ and Bergman spaces $A^p$, $1<p<\infty$, on the unit ball in $\mathbb{C}^n$, as well as the Hardy space on the polydisk and half-space. In particular, we show how the framework leads to a procedure to find a minimal norm element $f$ satisfying interpolation conditions $f(z_j)=w_j$, $j=1,\ldots , n$. We also explain the techniques in the setting of $\ell^p$ spaces where the norm is defined via a change of variables and provide numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11473 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal interpolation in Hardy and Bergman spaces: a reproducing kernel Banach space approach Groenewald, Gilbert J. ter Horst, Sanne Woerdeman, Hugo J. Functional Analysis 46E15, 42B30, 30H10, 46B10, 46B25 After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the setting of Hardy spaces $H^p$ and Bergman spaces $A^p$, $1<p<\infty$, on the unit ball in $\mathbb{C}^n$, as well as the Hardy space on the polydisk and half-space. In particular, we show how the framework leads to a procedure to find a minimal norm element $f$ satisfying interpolation conditions $f(z_j)=w_j$, $j=1,\ldots , n$. We also explain the techniques in the setting of $\ell^p$ spaces where the norm is defined via a change of variables and provide numerical examples. |
| title | Optimal interpolation in Hardy and Bergman spaces: a reproducing kernel Banach space approach |
| topic | Functional Analysis 46E15, 42B30, 30H10, 46B10, 46B25 |
| url | https://arxiv.org/abs/2412.11473 |