A Fourier integral formula for logarithmic energy
Leonhard Frerick, J\"urgen M\"uller, and Tobias Thomaser
TL;DR
This paper derives a Fourier integral formula to compute the logarithmic energy of measures in R^n, providing a new analytical tool and revisiting known formulas for Riesz energy with similar techniques.
Contribution
It introduces a novel Fourier integral representation for logarithmic energy and rederives a known Riesz energy formula using similar methods.
Findings
Established a Fourier integral formula for logarithmic energy.
Reinvented a known formula for Riesz energy using similar techniques.
Provided applications of the new formula in potential theory.
Abstract
A formula which expresses logarithmic energy of Borel measures on 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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Taxonomy
Topicsadvanced mathematical theories · Algebraic and Geometric Analysis · Mathematical functions and polynomials