Advanced Search

For a regular, compact, polynomially convex circled set $K$ in ${\mathbf{C}}^2$, we construct a sequence of pairs $\{P_n,Q_n\}$ of homogeneous polynomials in two variables with $\mathrm{deg}{P}_n=$ $\mathrm{deg}{Q}_n=n$ such that the sets $K_n:=\{(z,w)\in {\mathbf{C}}^2:|P_n(z,w)|\le 1,|Q_n(z,w)|\le 1\}$ approximate $K$ and if $K$ is the closure of a strictly pseudoconvex domain the normalized counting measures associated to the finite set $\{P_n=Q_n=1\}$ converge to the pluripotential-theoretic Monge-Ampère measure for $K$. The key ingredient is an approximation theorem for subharmonic functions of logarithmic growth in one complex...