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arXiv · 2412.11473

Optimal interpolation in Hardy and Bergman spaces: a reproducing kernel Banach space approach

Gilbert J. Groenewald·Sanne ter Horst·Hugo J. Woerdeman
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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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Gilbert J. Groenewald, Sanne ter Horst, Hugo J. Woerdeman. 2024-12-16. Optimal interpolation in Hardy and Bergman spaces: a reproducing kernel Banach space approach. https://arxiv.org/abs/2412.11473

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