A Fourier series formula for energy of measures with applications to Riesz products
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- by Kathryn E. Hare and Maria Roginskaya PDF
- Proc. Amer. Math. Soc. 131 (2003), 165-174 Request permission
Abstract:
In this paper we derive a formula relating the energy and the Fourier transform of a finite measure on the $d$-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.References
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Additional Information
- Kathryn E. Hare
- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
- MR Author ID: 246969
- Email: kehare@uwaterloo.ca
- Maria Roginskaya
- Affiliation: Department of Mathematics, Chalmers TH and Goteborg University, Eklandagatan 86, SE-41296, Sweden
- Email: maria@math.chalmers.se
- Received by editor(s): August 17, 2001
- Published electronically: June 12, 2002
- Additional Notes: This research was done while the first author enjoyed the hospitality of the Department of Mathematics at Göteborg University and Chalmers Institute of Technology. It was supported in part by NSERC and the Swedish Natural Sciences Research Council.
- Communicated by: David Preiss
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 165-174
- MSC (2000): Primary 28A12, 42A55
- DOI: https://doi.org/10.1090/S0002-9939-02-06826-0
- MathSciNet review: 1929036