A characterization of holomorphic bivariate functions of bounded index

Document Type

Article

Publication Date

6-27-2017

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 max{l:0≤l≤N} 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 max{(k,l):0,0≤k,l≤M,NUsing this notion we present necessary and sufficient conditions that ensure that a holomorphic bivariate function is of bounded index.

Publication Title

Mathematica Slovaca

Volume

67

Issue

3

First Page

731

Last Page

736

Digital Object Identifier (DOI)

10.1515/ms-2017-0005

ISSN

01399918

E-ISSN

13372211

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