Abstract
The main purpose of this paper is the following algebraic generalization of the corona theorem for the disc algebra\(A(\bar D)\): Ifd is a greatest common divisor of the functions\(f_1 ,...,f_n \in A(\bar D)\), then there exist functions\(g_1 ,...,g_n \in A(\bar D)\) withd=f1g1+...+fngn. This generalization is false for many algebras of holomorphic functions, e. g. in case of the Banach algebraH∞. Under the assumption that a greatest common divisord exists, also a description ofd is given.
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