Vol. 15, No. 3, 1965

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A nonnormal Blaschke-quotient

Joseph A. Cima

Vol. 15 (1965), No. 3, 767–773

We shall call the meromorphic functions of the form F(z) = B1(z)∕B2(z) Blaschke-quotients, where B1(z) and B2(z) are Blaschke products in |z| < 1 with zeros at {an} and {bk} respectively. Although there is a characterization of meromorphic functions which are normal there is no characterization of the Blaschke-quotients which are normal in terms of the non-Euclidean (hyperbolic) distances between the zeros {an} and {bk}. In this paper we show by construction that even if the zeros of a Blaschke-quotient are separated by a positive non-Euclidean distance the Blaschke-quotient need not be normal.

Mathematical Subject Classification
Primary: 30.65
Received: 17 April 1964
Revised: 3 August 1964
Published: 1 September 1965
Joseph A. Cima
Mathematics Department
The University of North Carolina at Chapel Hill
Chapel Hill NC
United States