A Family of Optimal Conditions for the Absence of Bound States in a Potential
One gives a general definition of capacity which includes -capacity, extremal length and a quantity defined by N.G. Meyers.
For potentials , where and are certain Schwartz distributions, an inversion formula for is derived. Convolutions and Fourier transforms of distributions in -spaces are used. It is shown that the equilibrium distribution with respect to the Riesz kernel of order , , of a compact subset of has the following property: its restriction to the interior of is an absolutely continuous measure with analytic density which is expressed by an explicit formula.