Whitney’s extension theorem for ultradifferentiable functions of Beurling type

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43941/1/11512_2006_Article_BF02386123.pd

MOMENT INEQUALITIES FOR EQUILIBRIUM MEASURES IN THE PLANE

Dedicated to our friend Fred Gehring, on the occasion of his 80th birthday ABSTRACT. The equilibrium measure of a compact plane set gives the steady state distribution of charges on the conductor. We show that certain moments of this equilibrium measure, when taken about the electrostatic centroid and depending only on the real coordinate, are extremal for an interval centered at the origin. This has consequences for means of zeros of polynomials, and for means of critical points of Green’s functions. We also study moments depending on the distance from the centroid, such as the electrostatic moment of inertia. 1