Analytic multifunctions, the ∂-equation, and a proof of the corona theorem

Bo Berndtsson and Thomas Joseph Ransford

Vol. 124 (1986), No. 1, 57–72

DOI: 10.2140/pjm.1986.124.57

Abstract

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 ∂-equation.

Mathematical Subject Classification 2000

Primary: 30D55

Secondary: 32E05, 46H05, 46J15

Milestones

Received: 11 April 1985

Published: 1 September 1986