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<p>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.</p>

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The Mercer-Young theorem for matrix-valued kernels on separable metric spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月18日

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  • Eyal Neuman,
  • Sturmius Tuschmann

摘要

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.