Vector-valued bivariate entire functions of bounded index satisfying a system of differential equations

Abstract

The concept of complex valued bivariate entire functions of bounded index is extended to C^n valued bivariate entire functions by replacing the absolute value in the definition of an entire function of bounded index by the maximum of the absolute values of the components. If the components of a C^n-valued bivariate entire function are of bounded index, then the function is also of bounded index. We present sufficient conditions providing index boundedness of bivariate vector-valued entire solutions of certain system of partial differential equations.