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arXiv · 1804.03047

Positive definite functions on semilattices

Vesa Kaarnioja·Pentti Haukkanen·Pauliina Ilmonen·Mika Mattila
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Abstract

We introduce a notion of positive definiteness for functions $f\!:P\to\mathbb{R}$ defined on meet semilattices $(P,\preceq,\wedge)$ and prove several properties for these functions. In addition, we utilize the $LDL^{\rm T}$ decomposition of meet matrices in order to explore the properties of multivariate positive definite arithmetic functions $f\!:\mathbb{Z}_+^d\to\mathbb{R}$. Finally, we give a series of examples and counterexamples of positive definite functions.

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Vesa Kaarnioja, Pentti Haukkanen, Pauliina Ilmonen, Mika Mattila. 2018-04-09. Positive definite functions on semilattices. https://arxiv.org/abs/1804.03047

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