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.
KeywordsCompact Subset Closed Subset Complex Manifold Plurisubharmonic Function Stein Manifold
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