An exceptional set for inner functions
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- by Renate McLaughlin PDF
- Proc. Amer. Math. Soc. 30 (1971), 545-546 Request permission
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
- E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR 0231999
- Einar Hille, Analytic function theory. Vol. 1, Introductions to Higher Mathematics, Ginn and Company, Boston, 1959. MR 0107692 G. Hössjer and O. Frostman, Über die Ausnahmestellen eines Blaschkeproduktes, Kungl. Fysiogr. Sällsk. Lund Förh. 3 (1933), no. 16, 8 pp.
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 545-546
- MSC: Primary 30.61
- DOI: https://doi.org/10.1090/S0002-9939-1971-0281922-3
- MathSciNet review: 0281922