二元指数型整函数的Carlson定理  

Theorem of Carlson for Binary Entire Functions of Exponential Type

作　　者：陈佳 康淑瑰 CHEN Jia;KANG Shu-gui(School of Mathematics and Statistics Science,Shanxi Datong University,Datong Shanxi,037009)

机构地区：[1]山西大同大学数学与统计学院,山西大同037009

出　　处：《山西大同大学学报（自然科学版）》2022年第3期19-22,共4页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：国家自然科学基金项目[11871314][12001342];山西省应用基础研究计划面上青年基金项目[201901D211440];山西省高等学校科技创新项目[2020L0464];大同市应用基础研究计划项目[2020154];山西大同大学博士科研启动经费[2019-B-10]。

摘　　要：指数型整函数的Carlson定理是函数逼近问题中的重要定理。将一维空间中的Carlson定理推广到二维空间中,并利用复分析的方法研究了二元指数型整函数的Carlson定理。得到如下结论:如果二维复数域上的指数型整函数在整数点处的函数值、一阶偏导数、二阶偏导数及三阶偏导数值都为0,那么该函数可以分解为指数型整函数与三角函数的乘积。特别地,如果满足上述条件的指数型整函数在二维实数域上有界,那么该指数型整函数可以由一个三角函数完全确定。Theorem of Carlson for entire functions of exponential type is an important theorem on approximation problem.In this paper,we deduce the Carlson’s theorem from one dimensional function space to two dimensional function space,and investigate Carlson’s theorem of binary entire functions of exponential type by the method of complex analysis.We obtain that if an entire function in two dimensional complex field is equal to zero on its function values,first-order partial derivatives,second-order partial derivatives and third-order partial derivatives at all integers,then the function is equal to an entire function times a trigonometric function.Especially,if the exponential type of the above function is bounded in two dimensional real field,then the function is completely determined by a trigonometric function.

关 键 词：二元指数型整函数 Carlson定理 复分析 高阶偏导数 

分 类 号：O174.56[理学—数学]