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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Asymptotic values of modulus $1$ of Blaschke products

Authors: K. K. Leung and C. N. Linden
Journal: Trans. Amer. Math. Soc. 203 (1975), 107-118
MSC: Primary 30A72; Secondary 30A76
MathSciNet review: 0361084
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Abstract: A sufficient condition is found for each subproduct of a Blaschke product to have an asymptotic value of modulus 1 along a prescribed arc of a specified type in the unit disc. The condition obtained is found to be necessary in the case of further restrictions of the arc, and the two results give rise to a necessary and sufficient condition for the existence of ${T_\gamma }$-limits of modulus 1 for Blaschke products.

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Keywords: Blaschke products, <!– MATH ${T_\gamma }$ –> <IMG WIDTH="28" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${T_\gamma }$">-limits
Article copyright: © Copyright 1975 American Mathematical Society