Small Ball and Discrepancy Inequalities
Classical Analysis and ODEs
2007-05-23 v1 Number Theory
Abstract
This is a comprehensive set of notes on the ArXiV paper math.CA/0609815 by Dmitry Bilyk and the author. The focus of that paper is a new inequality for sums of hyperbolic Haar functions in three variables, extending a famous result of J Beck from 1987. This is an improvement on what is known as the Small Ball Conjecture. In this paper, that result is proved, in a more leisurely fashion and additional remarks. In addition, background material is gathered together, including a complete proof of the necessary Harmonic Analysis; a summary of known results on the Small Ball inequality; Irregularities of Distribution; the relationship with conjectures in Approximation Theory and Probability Theory.
Keywords
Cite
@article{arxiv.math/0609816,
title = {Small Ball and Discrepancy Inequalities},
author = {Michael T Lacey},
journal= {arXiv preprint arXiv:math/0609816},
year = {2007}
}
Comments
73 pages