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On a class of functions regular in the unit disc

Published online by Cambridge University Press:  24 October 2008

R. Hornblower
R. Hornblower
Affiliation:
Imperial College, London
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Extract

MacLane(1) has introduced the class of functions with a dense set of asymptotic values on {|z| = 1} in the following sense:

Definition. Let f(z) be regular and not constant in the unit disc and let ξ be a point of {|z| = 1}. Suppose that there exists a curve Γξ in {|z| < 1} and a in the closed complex plane such that f(z) → a as z → ξ along Γξ. Then we say ξ ∈ Aa.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 3 , July 1968 , pp. 651 - 654
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)MacLane, G. R.Asymptotic values of holomorphic functions. Rice Univ. Studies, 49, no. 1 (1963), 83 pp.Google Scholar
(2)Polya, G. and Szegö, G.Aufgaben und Lehrsatz aus der Analysis II.Google Scholar
(3)Valiron, G.Sur les singularités de certaines fonctions holomorphes et de leurs inverses. J. Math. Pures Appl. (9) 15 (1936), 423–435.Google Scholar