Anti-uniformity norms, anti-uniformity functions and their algebras on Euclidean spaces
A. Martina Neuman

TL;DR
This paper investigates the structure of anti-uniform functions and their algebras on Euclidean spaces, focusing on approximation by Gowers-Host-Kra dual functions and the algebraic properties of generalized cubic convolution products.
Contribution
It introduces a framework for understanding anti-uniformity norms and functions on Euclidean spaces, and explores their algebraic structures and approximation properties.
Findings
Anti-uniform functions can be approximated by Gowers-Host-Kra dual functions.
Generalized cubic convolution products form specific algebraic structures.
The paper characterizes the algebraic properties of anti-uniformity on Euclidean spaces.
Abstract
Let be an integer. Given a uniform function - one that satisfies , there is an associated anti-uniform function - one that satisfied . The question is, can one approximate with the Gowers-Host-Kra dual function of ? Moreover, given the generalized cubic convolution products , what sorts of algebras can they form? In short, this paper explores possible structures of anti-uniformity on Euclidean spaces.
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Taxonomy
TopicsAdvanced Banach Space Theory · Limits and Structures in Graph Theory · Advanced Harmonic Analysis Research
