Analytic multifunctions, the<ovl><i>∂</i></ovl>-equation, and a proof of the corona theorem

The purpose of this article is to give some applications of a recent theorem by Alexander-Wermer and Slodkowski on the structure of certain polynomial hulls. We want to show that this theorem gives a useful method of constructing analytic functions with prescribed properties in the disc. In particular it yields a rather easy proof of the Corona Theorem for two generators, and also implies Wolff's Theorem on the d-equation.

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