Some characterizations of semi-Bloch functions

Aulaskari, Rauno; Lappan, Peter

doi:10.1090/S0002-9939-1993-1165046-3

Some characterizations of semi-Bloch functions
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by Rauno Aulaskari and Peter Lappan PDF

Proc. Amer. Math. Soc. 119 (1993), 1233-1238 Request permission

Abstract:

A function $f$ analytic in the unit disk is called a semi-Bloch function if, for each complex number $\lambda$, the function ${g_\lambda }(z) = \exp (\lambda f(z))$ is a normal function. We give both an analytic and a geometric characterization of semi-Bloch functions, together with some examples to show that semi-Bloch functions are not closed under either addition or multiplication.

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