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

DOI:
https://doi.org/10.1090/S0002-9939-03-07238-1

Published electronically:
August 12, 2003

MathSciNet review:
2022362

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Abstract | References | Similar Articles | Additional Information

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

Email:
kehare@uwaterloo.ca

**Maria Roginskaya**

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

Email:
maria@math.chalmers.se

DOI:
https://doi.org/10.1090/S0002-9939-03-07238-1

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