Abstract
We establish that, for a Blaschke product B(z) convergent in the unit disk, the condition - ∞ <\(\smallint _0^1 \log (1 - t)n(t,B)dt\) is sufficient for the total variation of logB to be bounded on a circle of radiusr, 0 <r < 1. For products B(z) with zeros concentrated on a single ray, this condition is also necessary. Here, n(t, B) denotes the number of zeros of the functionB (z) in a disk of radiust.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 11, pp. 1449–1455, November, 1999.
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Vasyl’kiv, Y.V. On the boundedness of the total variation of the logarithm of a Blaschke product. Ukr Math J 51, 1635–1642 (1999). https://doi.org/10.1007/BF02525267
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DOI: https://doi.org/10.1007/BF02525267