Polynomials associated to non-convex bodies

Abstract

Polynomial spaces associated to a convex body C in (R + ) d have been the object of recent studies. In this work, we consider polynomial spaces associated to non-convex C. We develop some basic pluripotential theory including notions of C−extremal plurisubharmonic functions VC,K for K ⊂ C d compact. Using this, we discuss Bernstein-Walsh type polynomial approximation results and asymptotics of random polynomials in this non-convex setting.