Generalizations of Fourier analysis, and how to apply them

2016/08/14 by W. T. Gowers, Gowers, W. T. · 1 citation
Computer Science · Mathematics · #05-02 #43-02 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1608.04127

openalex publication_date 2016/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a survey of the use of Fourier analysis in additive combinatorics, with a particular focus on situations where it cannot be straightforwardly applied, but needs to be generalized first. Sometimes very satisfactory generalizations exist, while sometimes we have to make do with theories that have some of the desirable properties of Fourier analysis but not all of them. In the latter case, there are intriguing hints that there may be more satisfactory theories yet to be discovered. This article grew out of the Colloquium Lectures at the Joint Meeting of the AMS and the MAA, given in Seattle in January 2016.

Citations

• Nilspaces, nilmanifolds and their morphisms
• Structure of finite nilspaces and inverse theorems for the Gowers norms in bounded exponent groups
• Roth’s theorem on progressions revisited
• On Certain Sets of Integers

Cited by

• Pseudorandom bits for non-commutative programs

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