The Mercer-Young Theorem for Matrix-Valued Kernels on Separable Metric Spaces
Functional Analysis
2025-10-09 v2 Optimization and Control
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.
Keywords
Cite
@article{arxiv.2403.18368,
title = {The Mercer-Young Theorem for Matrix-Valued Kernels on Separable Metric Spaces},
author = {Eyal Neuman and Sturmius Tuschmann},
journal= {arXiv preprint arXiv:2403.18368},
year = {2025}
}
Comments
17 pages, 2 figures