Sums of functions of bounded index

Abstract

Introduction. The notion of entire functions of bounded index has been studied by several authors in a number of recent papers [1], [2], [3], [4]. Little is known about the properties of such functions, and, in particular, the following natural question (which is answered in this note) does not appear to have been studied. Is the sum of two functions of bounded index also of bounded index? Let g(z) be an entire function. We write as usual