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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.18368 |
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| _version_ | 1866915537179639808 |
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| author | Neuman, Eyal Tuschmann, Sturmius |
| author_facet | Neuman, Eyal Tuschmann, Sturmius |
| contents | We generalize the characterization theorem going back to Mercer and Young, which states that a symmetric and continuous kernel is positive definite if and only if it is integrally positive definite, to matrix-valued kernels on separable metric spaces. We also demonstrate the applications of the generalized theorem to the field of convex optimization and other areas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Mercer-Young Theorem for Matrix-Valued Kernels on Separable Metric Spaces Neuman, Eyal Tuschmann, Sturmius Functional Analysis Optimization and Control 28A25, 43A35, 47B34 We generalize the characterization theorem going back to Mercer and Young, which states that a symmetric and continuous kernel is positive definite if and only if it is integrally positive definite, to matrix-valued kernels on separable metric spaces. We also demonstrate the applications of the generalized theorem to the field of convex optimization and other areas. |
| title | The Mercer-Young Theorem for Matrix-Valued Kernels on Separable Metric Spaces |
| topic | Functional Analysis Optimization and Control 28A25, 43A35, 47B34 |
| url | https://arxiv.org/abs/2403.18368 |