A characterization of functions with vanishing averages over products of disjoint sets. (August 2016)

• Record Type: Journal Article
• Authors: Hatami, Hamed; Hatami, Pooya; Li, Yaqiao
• Is Part Of: European journal of combinatorics. Volume 56(2016:Aug.)
• Page Start: 81
• Page End: 93
• Publication Date: 2016-08
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2016.03.002
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: Given α 1, …, α m ∈ ( 0, 1 ), we characterize all integrable functions f : [ 0, 1 ] m → C satisfying ∫ A 1 × ⋯ × A m f = 0 for any collection of disjoint measurable sets A 1, …, A m ⊆ [ 0, 1 ] of respective measures α 1, …, α m . We use this characterization to settle some of the conjectures in Janson and Sós (2015) about the relation between subgraph counts and quasi-randomness.