Embeddings of Reproducing Kernel Hilbert Spaces with General Weights

Michael Gnewuch; Peter Kritzer; Klaus Ritter

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arXiv · 2604.27160

Embeddings of Reproducing Kernel Hilbert Spaces with General Weights

Michael Gnewuch·Peter Kritzer·Klaus Ritter

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Abstract

We study embeddings between reproducing kernel Hilbert spaces $H(K)$ of functions of $d \in \mathbb{N} \cup \{\infty\}$ variables. The kernels $K$ are superpositions of weighted finite tensor products of a fixed univariate kernel. The basic idea for the embeddings is to compensate a change of the univariate kernel by a suitable transformation of the weights. For the proofs we employ ($d \in \mathbb{N}$) and develop ($d = \infty$) a discrete calculus on the cone of all weights, where completely monotone weights play a particular role. We sketch how to apply the embedding results to computational problems, as, e.g., numerical integration or function recovery.

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Michael Gnewuch, Peter Kritzer, Klaus Ritter. 2026-04-29. Embeddings of Reproducing Kernel Hilbert Spaces with General Weights. https://arxiv.org/abs/2604.27160

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