Positive definite functions on semilattices

2018/04/09 by Vesa Kaarnioja, Kaarnioja, Vesa, Pentti Haukkanen +5
Computer Science · Decision Sciences · #06A12 #11A25 #11C20 #15A69 #15B36 #Advanced Algebra and Logic #Combinatorics (math.CO) #FOS: Mathematics #Fuzzy and Soft Set Theory #Multi-Criteria Decision Making #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1804.03047

openalex publication_date 2018/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a notion of positive definiteness for functions f :P→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 :ℤ₊^d→ℝ. Finally, we give a series of examples and counterexamples of positive definite functions.

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