Approximation

Abstract

The present chapter is devoted in the main to some approximation theorems for continuous functions defined on totally real sets. The approximation results established here are of a global nature. Section 6.1 contains preparatory material on totally real sets and manifolds. Section 6.2 introduces holomorphically convex compacta and develops some of their main properties. Section 6.3 contains a result on uniform approximation on compacta in totally real sets. Section 6.4 presents some material on the algebras ℛ(X) for planar compacta X for use in the following section. Section 6.5 considers algebras on smooth manifolds and analytic varieties. Section 6.6 contains results on tangential approximation.