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Proceedings of the American Mathematical Society

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The energy of signed measures

Authors: Kathryn E. Hare and Maria Roginskaya
Journal: Proc. Amer. Math. Soc. 132 (2004), 397-406
MSC (2000): Primary 28A12; Secondary 42B10
Published electronically: August 12, 2003
MathSciNet review: 2022362
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Abstract: We generalize the concept of energy to complex measures of finite variation. We show that although the energy dimension of a measure can exceed that of its total variation, it is always less than the Hausdorff dimension of the measure. As an application we prove a variant of the uncertainty principle.

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Additional Information

Kathryn E. Hare
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

Maria Roginskaya
Affiliation: Department of Mathematics, Chalmers TH and Goteborg University, Eklandagatan 86, SE 412 96, Sweden

Keywords: Energy, Hausdorff dimension, uncertainty principle
Received by editor(s): September 20, 2002
Published electronically: August 12, 2003
Additional Notes: Part of this research was done while the first author enjoyed the hospitality of the Departments of Mathematics of Goteborg University and Chalmers Institute of Technology and the University of Hawaii. It was supported in part by NSERC and the Swedish natural sciences research council.
Communicated by: David Preiss
Article copyright: © Copyright 2003 American Mathematical Society