A characterization of holomorphic bivariate functions of bounded index

Abstract

The following notion of bounded index for complex entire functions was presented by Lepson. function f(z) is of bounded index if there exists an integer N independent of z, such that The main goal of this paper is extend this notion to holomorphic bivariate function. To that end, we obtain the following definition. A holomorphic bivariate function is of bounded index, if there exist two integers M and N such that M and N are the least integers such that Using this notion we present necessary and sufficient conditions that ensure that a holomorphic bivariate function is of bounded index.