Jensen measures and annihilators of holomorphic functions

Abstract

For a relatively compact domain $M$ in a complex manifold, we completely characterize in terms of Jensen measures the annihilating measures of the algebra $A(\overline M)$ of holomorphic functions and the space $h(\overline M)$ of pluriharmonic functions continuous on $\overline M$. We also establish the equivalence of Mergelyan type approximation properties of a domain for different function spaces.