Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.27160 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918474893230080 |
|---|---|
| author | Gnewuch, Michael Kritzer, Peter Ritter, Klaus |
| author_facet | Gnewuch, Michael Kritzer, Peter Ritter, Klaus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27160 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Embeddings of Reproducing Kernel Hilbert Spaces with General Weights Gnewuch, Michael Kritzer, Peter Ritter, Klaus Numerical Analysis 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. |
| title | Embeddings of Reproducing Kernel Hilbert Spaces with General Weights |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.27160 |