Small Ball and Discrepancy Inequalities
| dc.creator | Lacey, Michael T | |
| dc.date | 2006-09-28 | |
| dc.date.accessioned | 2026-07-07T07:25:24Z | |
| dc.date.available | 2026-07-07T07:25:24Z | |
| dc.description | 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. | |
| dc.description | 73 pages | |
| dc.identifier | https://arxiv.org/abs/math/0609816 | |
| dc.identifier | http://arxiv.org/abs/math/0609816 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116706 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Number Theory | |
| dc.subject | 11K38, 60G15 | |
| dc.title | Small Ball and Discrepancy Inequalities | |
| dc.type | text |