paper

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

arXiv:2403.18368 · doi:10.1007/s11117-025-01123-1

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.

17 pages, 2 figures

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