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1996•Pacific Journal of MathematicsOpen access

Interpolating Blaschke products

Donald E. Marshall, Arne Stray

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Abstract

We prove that any bounded analytic function on the unit disk D which extends to be continuous on dD \ E, for some set E of measure 0, can be uniformly approximated by finite linear combinations of interpolating Blaschke products.Let H°° denote the set of bounded analytic functions defined on the unit disk, D. Each / G H°° has a non-tangential limit at almost all e iθ G dD which we call f(e tθ ), and Anal., 21 (1976), 380-388.

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We prove that any bounded analytic function on the unit disk D which extends to be continuous on dD \ E, for some set E of measure 0, can be uniformly approximated by finite linear combinations of interpolating Blaschke products.Let H°° denote the set of bounded analytic functions defined on the unit disk, D. Each / G H°° has a non-tangential limit at almost all e iθ G dD which we call f(e tθ ), and Anal., 21 (1976), 380-388.

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We prove that any bounded analytic function on the unit disk D which extends to be continuous on dD \ E, for some set E of measure 0, can be uniformly approximated by finite linear combinations of interpolating Blaschke products.Let H°° denote the set of bounded analytic functions defined on the unit disk, D. Each / G H°° has a non-tangential limit at almost all e iθ G dD which we call f(e tθ ), and Anal., 21 (1976), 380-388.

Key concepts: Blaschke product, Mathematics, Hardy space, Inner product space, Linear subspace, Invariant (physics), Pure mathematics, Subalgebra

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