A point of view on Gowers uniformity norms - Archive ouverte HAL Access content directly
Journal Articles New York Journal of Mathematics Year : 2012

A point of view on Gowers uniformity norms

Abstract

Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of focusing on the norms themselves, we study associated dual norms and dual functions. Combining this study with a variant of the Szemerédi Regularity Lemma, we give a decomposition theorem for dual functions, linking the dual norms to classical norms and indicating that the dual norm is easier to understand than the norm itself. Using the dual functions, we introduce higher order algebras that are analogs of the classical Fourier algebra, which in turn can be used to further characterize the dual functions.
Fichier principal
Vignette du fichier
gowersnorms-new1.pdf (374.11 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00735476 , version 1 (25-09-2012)

Identifiers

  • HAL Id : hal-00735476 , version 1

Cite

Bernard Host, Bryna Kra. A point of view on Gowers uniformity norms. New York Journal of Mathematics, 2012, 18, pp.213-248. ⟨hal-00735476⟩
167 View
110 Download

Share

Gmail Facebook X LinkedIn More