An inversion formula and a note on the Riesz kernel

Dunkels, Andrejs. "An inversion formula and a note on the Riesz kernel." Annales de l'institut Fourier 26.4 (1976): 197-205. <http://eudml.org/doc/74299>.

@article{Dunkels1976,
abstract = {For potentials $U^T_K=K*T$, where $K$ and $T$ are certain Schwartz distributions, an inversion formula for $T$ is derived. Convolutions and Fourier transforms of distributions in $(\{\bf D\}^\{\prime \}_Lp)$-spaces are used. It is shown that the equilibrium distribution with respect to the Riesz kernel of order $\alpha $, $0&lt; \alpha &lt; m$, of a compact subset $E$ of $\{\bf R\}^m$ has the following property: its restriction to the interior of $E$ is an absolutely continuous measure with analytic density which is expressed by an explicit formula.},
author = {Dunkels, Andrejs},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {4},
pages = {197-205},
publisher = {Association des Annales de l'Institut Fourier},
title = {An inversion formula and a note on the Riesz kernel},
url = {http://eudml.org/doc/74299},
volume = {26},
year = {1976},
}

TY - JOUR
AU - Dunkels, Andrejs
TI - An inversion formula and a note on the Riesz kernel
JO - Annales de l'institut Fourier
PY - 1976
PB - Association des Annales de l'Institut Fourier
VL - 26
IS - 4
SP - 197
EP - 205
AB - For potentials $U^T_K=K*T$, where $K$ and $T$ are certain Schwartz distributions, an inversion formula for $T$ is derived. Convolutions and Fourier transforms of distributions in $({\bf D}^{\prime }_Lp)$-spaces are used. It is shown that the equilibrium distribution with respect to the Riesz kernel of order $\alpha $, $0&lt; \alpha &lt; m$, of a compact subset $E$ of ${\bf R}^m$ has the following property: its restriction to the interior of $E$ is an absolutely continuous measure with analytic density which is expressed by an explicit formula.
LA - eng
UR - http://eudml.org/doc/74299
ER -