Parseval-type identities for Gowers uniformity norms in finite abelian groups

2025/08/12 by Martin Niepel, Niepel, Martin
Mathematics · #11B30 #43A25 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Combinatorics (math.CO) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2508.08968

openalex publication_date 2025/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Orthogonality relations for cubes of characters in Gowers inner products ⟨ ⋅ ⟩_d,l lead to Parseval-type identities and isometries for suitably generalized Gowers uniformity norms U^d,l.

Citations

• Fourier duality in the Brascamp-Lieb inequality
• Singular Brascamp-Lieb: a survey
• Nilspace factors for general uniformity seminorms, cubic exchangeability and limits
• Gowers norms, regularization and limits of functions on abelian groups
• Nilspaces, nilmanifolds and their morphisms
• Parallelepipeds, Nilpotent Groups, and Gowers Norms

Related

• The inverse theorem for the U³ Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches
• Gowers norms for singular measures
• Structure of finite nilspaces and inverse theorems for the Gowers norms\n in bounded exponent groups
• A Correspondence Principle for the Gowers Norms
• Parallelepipeds, Nilpotent Groups, and Gowers Norms