科研之友
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摘要
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}) {vertical bar f((l)) (z)vertical bar/l!} >= vertical bar f((n)) (z)vertical bar/n! for all 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,N}) {vertical bar f((k,l)) (z,w)vertical bar/k!l!} >= vertical bar f((m,n)) (z,w)vertical bar/m!n! for all m and n. Using this notion we present necessary and sufficient conditions that ensure that a holomorphic bivariate function is of bounded index.
- 出版日期2017-6
