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Radial and Angular Limits of Meromorphic Functions

Published online by Cambridge University Press:  20 November 2018

G. T. Cargo
G. T. Cargo*
Affiliation:
Syracuse University
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Let us say that a function denned in the open unit disk D has the Montel property if the set of those points eiθ on the unit circle C where the radial limit exists coincides with the set where the angular limit exists. By a classical theorem of Montel (4), every bounded holomorphic function has this property. Meromorphic functions omitting at least three values and, more generally, the normal functions recently introduced by Lehto and Virtanen (3) also enjoy the Montel property (also see 1).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 471 - 474
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Bagemihl, F. and Seidel, W., Sequential and continuous limits of meromorphic functions, Ann. Acad. Sci. Fenn., Ser. A, I, 280 (1960).Google Scholar
2. Lappan, P., Non-normal sums and products of unbounded normal functions, Michigan Math. J., 8 (1961), 187–192.Google Scholar
3. Lehto, O. and Virtanen, K. I., Boundary behaviour and normal meromorphic functions, Acta Math., 97 (1957), 47–65.Google Scholar
4. Montel, P., Sur les familles de fonctions analytiques qui admettent des valeurs exceptionnelles dans un domaine, Ann. sci. école norm, sup., 29 (1912), 487–535.Google Scholar