Abstract
A formula which expresses logarithmic energy of Borel measures on \(\mathbb {R}^n\) in terms of the Fourier transforms of the measures is established and some applications are given. In addition, using similar techniques a (known) formula for Riesz energy is reinvented.
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Acknowledgements
The authors are grateful to Lutz Mattner, Norbert Ortner, Peter Wagner and Jochen Wengenroth for several helpful comments. Special thanks to Norbert Ortner for his letter containing a number of highly valuable informations and suggestions around the subject and also to the referee for his fruitful comments.
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Frerick, L., Müller, J. & Thomaser, T. A Fourier Integral Formula for Logarithmic Energy. Potential Anal (2024). https://doi.org/10.1007/s11118-024-10125-9
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DOI: https://doi.org/10.1007/s11118-024-10125-9