On a theorem of Hayman concerning the derivative of a function of bounded characteristic

Patrick Robert Ahern

Vol. 83 (1979), No. 2, 297–301

DOI: 10.2140/pjm.1979.83.297

Abstract

W. Hayman [On Nevanlinna’s second theorem and extensions, Rend. Circ. Mat. Palermo, Ser. II, II (1953).] has given sufficient conditions on a function, f, of bounded characteristic in the unit disc, in order that f′ also have bounded characteristic. In this paper it is shown that one of these conditions is also necessary for the conclusion of the theorem to hold.

Mathematical Subject Classification 2000

Primary: 30D50

Milestones

Received: 1 January 1979

Published: 1 August 1979