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Proceedings of the American Mathematical Society

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An exceptional set for inner functions

Author: Renate McLaughlin
Journal: Proc. Amer. Math. Soc. 30 (1971), 545-546
MSC: Primary 30.61
MathSciNet review: 0281922
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Abstract: Suppose f is an inner function that is not a constant and not a finite Blaschke product. Let $ E(f)$ denote the set of values inside the unit disk that are not assumed infinitely often by f. We show that $ E(f)$ is an $ {F_\sigma }$-set.

References [Enhancements On Off] (What's this?)

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  • [2] Einar Hille, Analytic function theory. Vol. 1, Introduction to Higher Mathematics, Ginn and Company, Boston, 1959. MR 0107692
  • [3] G. Hössjer and O. Frostman, Über die Ausnahmestellen eines Blaschkeproduktes, Kungl. Fysiogr. Sällsk. Lund Förh. 3 (1933), no. 16, 8 pp.

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Keywords: Inner function, values that an inner function assumes at most finitely often, $ {F_\sigma }$-set, Rouché's theorem
Article copyright: © Copyright 1971 American Mathematical Society

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