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An inversion formula and a note on the Riesz kernel

Andrejs Dunkels — 1976

Annales de l'institut Fourier

For potentials U K T = K * T , where K and T are certain Schwartz distributions, an inversion formula for T is derived. Convolutions and Fourier transforms of distributions in ( D L ' p ) -spaces are used. It is shown that the equilibrium distribution with respect to the Riesz kernel of order α , 0 < α < m , of a compact subset E of 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.

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