On some representation formulas involving moduli of Blaschke products

Alan Gluchoff, Pamela Gorkin and Raymond Mortini

Starting from an integral formula in harmonic analysis, we derive some representation formulas for (1–|B(z)|2)/(1–|z|2) in terms of the zeros of the underlying interpolating Blaschke product B. We use our formula to show that for every interpolating Blaschke product B there exists another interpolating Blaschke product C, with zeros distinct from those of B, such that C is orthogonal to B in H2.

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Analysis is devoted to the field of mathematical analysis, in particular classical analysis and its applications. Its aim is to publish the best research articles within the scope of the journal, as well as to boost the cooperation between scholars.