Decompositions, approximate structure, transference, and the Hahn-Banach theorem
Combinatorics
2014-02-26 v1 Functional Analysis
Abstract
This paper is partly a survey of certain kinds of results and proofs in additive combinatorics, and partly a discussion of how useful the finite-dimensional Hahn-Banach theorem can be. The most interesting single result is probably a simpler proof of a key step in the proof of the Green-Tao theorem, but several other applications of the method are given. A similarly simplified proof of the Green-Tao transference principle was obtained independently (and expressed in a rather different language) by Reingold, Trevisan, Tulsiani and Vadhan.
Cite
@article{arxiv.0811.3103,
title = {Decompositions, approximate structure, transference, and the Hahn-Banach theorem},
author = {W. T. Gowers},
journal= {arXiv preprint arXiv:0811.3103},
year = {2014}
}
Comments
48 pages