Abstract
The result by Bourgain that every unimodular function ψ \psi on the unit circle can be factored as ψ = e i v ~ B 1 B ¯ 2 \psi = e^{i \tilde v} B_1 \overline B_2 with B 1 B_1 and B 2 B_2 Blaschke products can be improved. We show that the same result holds with B 1 B_1 and B 2 B_2 interpolating Blaschke products. This will at the same time be a refinement of Jones’s result that every unimodular function can be approximated in the H ∞ H^\infty -norm by a ratio of interpolating Blaschke products.
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