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arXiv · 2603.26979

Characterization of the reproducing structure of the Bessel potential spaces beyond $p=2$

Tjeerd Jan Heeringa
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Abstract

Reproducing kernel Hilbert spaces are uniquely characterized by their kernel, but reproducing kernel Banach spaces (RKBS) are not. However, a characterization of which RKBS admit a given kernel as reproducing kernel is lacking. This work provides such a characterization for the well-known Bessel potential / Mat\`ern kernel, a widely used covariance kernel for Gaussian processes which is the reproducing kernel of the Bessel potential space $H^{s,2}(\mathbb{R}^d)$ when $s>d/2$. Concretely, this work characterizes the pairs of Bessel potential spaces $H^{u,p}(\mathbb{R}^d),H^{v,q}(\mathbb{R}^d)$ which have this kernel.

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Tjeerd Jan Heeringa. 2026-03-27. Characterization of the reproducing structure of the Bessel potential spaces beyond $p=2$. https://arxiv.org/abs/2603.26979

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