A Fourier series formula for energy of measures with applications to Riesz products期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

A Fourier series formula for energy of measures with applications to Riesz products

Authors:	Kathryn E Hare Maria Roginskaya

Institution:	Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 ; Department of Mathematics, Chalmers TH and Goteborg University, Eklandagatan 86, SE-41296, Sweden

Abstract:	In this paper we derive a formula relating the energy and the Fourier transform of a finite measure on the -dimensional torus which is similar to the well-known formula for measures on $\mathbb{R} ^{d}$ . We apply the formula to obtain estimates on the Hausdorff dimension of Riesz product measures. These give improvements on the earlier, classical results which were based on completely different techniques.

Keywords:	energy Hausdorff dimension Riesz products

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文