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Preprint
Optimal interpolation in Hardy and Bergman spaces: a reproducing kernel Banach space approach
IACAPAP ArXiv (Online)
16 Dec 2024
Abstract
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.
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Details
- Title
- Optimal interpolation in Hardy and Bergman spaces: a reproducing kernel Banach space approach
- Creators
- Gilbert J GroenewaldSanne ter HorstHugo J Woerdeman
- Publication Details
- IACAPAP ArXiv (Online)
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022005488104721