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arXiv · 2403.18368

The Mercer-Young Theorem for Matrix-Valued Kernels on Separable Metric Spaces

Eyal Neuman·Sturmius Tuschmann
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Abstract

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.

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Eyal Neuman, Sturmius Tuschmann. 2024-03-27. The Mercer-Young Theorem for Matrix-Valued Kernels on Separable Metric Spaces. https://doi.org/10.1007/s11117-025-01123-1

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