对数能量的傅立叶积分公式

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2024-02-09 DOI:10.1007/s11118-024-10125-9

L. Frerick, J. Müller, T. Thomaser

引用次数: 0

摘要

建立了一个用度量的傅里叶变换来表示 \mathbb {R}^n\ 上的博雷尔度量的对数能量的公式，并给出了一些应用。此外，还利用类似的技术重新发明了（已知的）里兹能量公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Fourier Integral Formula for Logarithmic Energy

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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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.