Polynomials associated to non-convex bodies (Q2064777)

Polynomial spaces associated to a non-convex body \(C\) in \((\mathbb{R}^{+})^d\) are studied, developing some basic pluripotential theory including notions of \(C\)-extremal plurisubharmonic functions \(V_{C,K}\) for \(K \subset \mathbb{C}^d\) compact. Bernstein-Walsh type polynomial approximation results and asymptotics of random polynomials in this non-convex setting are also discussed.