Positive definite functions on semilattices [article]

Vesa Kaarnioja and Pentti Haukkanen and Pauliina Ilmonen and Mika Mattila
2020 arXiv   pre-print
We introduce a notion of positive definiteness for functions f:P→R defined on meet semilattices (P,≼,∧) and prove several properties for these functions. In addition, we utilize the LDL^ T decomposition of meet matrices in order to explore the properties of multivariate positive definite arithmetic functions f:Z_+^d→R. Finally, we give a series of examples and counterexamples of positive definite functions.
arXiv:1804.03047v2 fatcat:lod22x7xmjfbpc5bmxp2t26uou