利用Green函数给出H^n[a,b]空间中再生核函数  

Using Green function to provide the reproducing kernel function in H^n [a,b] space

作　　者：徐亚兰[1] 马玉秋[1] 

机构地区：[1]哈尔滨学院理学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2013年第2期175-179,186,共6页Journal of Natural Science of Heilongjiang University

基　　金：黑龙江省教育厅科学技术研究项目(11553060)

摘　　要：利用线性微分算子和线性算子将Hn[a,b]空间进行直和分解,借助微分系统的Green函数和线性变换基本定理,构造出Hn[a,b]空间的两个正交子空间的再生核函数。根据再生核函数和的运算性质,给出Hn[a,b]空间中再生核函数的表达式,达到进一步了解Hn[a,b]空间结构的目的。为深入研究H4[0,1]再生核空间的性质提供了理论基础。The direct sum decomposition of the H^n [ a, b ] space was first given by using the linear ulnerenual opelutor and linear operator. According to the fundamental theorem of the linear transform and Green function of the differential system, the reproducing kernel functions of the two orthogonal subspaces were developed in the H^n [ a, b ] space. Finally according to the property of the sum of reproducing kernel functions, the expression of the reprodu- cing kernel function was developed in the Hn [ a, b ] space. This reaches the purpose of understanding structure of space, and provides the theoretical basis for the thorough research about the properties of the reproducing kernel space of Hn [ a, b ].

关 键 词：线性微分算子 GREEN函数 再生核函数 

分 类 号：O177[理学—数学]