Conditions for generating a nonvanishing bounded analytic function
Abstract: B. A. Taylor and L. A. Rubel have posed the problem of finding necessary and sufficient conditions on a set of given functions in such that there exist functions in with in the open unit disc. L. A. Rubel has conjectured that a necessary and sufficient condition is that there exist a harmonic minorant of in the open unit disc. The major result of this paper proves that the conjecture is true if one of the given functions has a zero set which is an interpolation set for .
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Keywords: Blaschke product, , interpolation sequence for , harmonic minorant, zero set, generating a nonvanishing bounded analytic function
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