Skip Navigation



Journal of the London Mathematical Society Advance Access published online on May 19, 2009
Journal of the London Mathematical Society, doi:10.1112/jlms/jdp016
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
80/1/72    most recent
jdp016v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Lefèvre, P.
Right arrow Articles by Rodríguez-Piazza, L.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2009 London Mathematical Society

Invariant means and thin sets in harmonic analysis with applications to prime numbers

Pascal Lefèvre

Univ Lille Nord de France F-59 000 LILLE U-Artois
Laboratoire de Mathématiques de Lens EA 2462
Fédération CNRS Nord-Pas-de-Calais FR 2956
F-62 300 LENS
France

Luis Rodríguez-Piazza

Faculdad de Matematica
Universidad de Sevilla
Apdo 1160
41080 Sevilla
Spain
piazza@us.es

We first prove a localization principle characterizing Lust-Piquard sets. We obtain that the union of two Lust-Piquard sets is a Lust-Piquard set, provided that one of these two sets is closed for the Bohr topology. We also show that the closure of the set of prime numbers is a Lust-Piquard set, generalizing results of Lust-Piquard and Meyer, and even that the set of integers whose expansion uses fewer than r factors is a Lust-Piquard set. On the other hand, we use random methods to prove that there are some sets that are UC, {Lambda}(q) for every q>2 and p-Sidon for every p>1, but which are not Lust-Piquard sets. This is a consequence of the fact that a uniformly distributed set cannot be a Lust-Piquard set.

2000 Mathematics Subject Classification 43A46 (primary), 42A20, 42A55, 43A77 (secondary).

This paper was partially supported by BFM2003-01297 and MTM2006-05622.

Received October 21, 2007; revised October 21, 2008;
Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.