再生核空间W2^1[a，b]中两个问题的讨论  

THE DISCUSSION OF TWO PROBLEMS IN A REPRODUCING KERNEL SPACE W_2~1

作　　者：杜红[1] 张晓光[2] 

机构地区：[1]黑龙江科技学院 [2]哈尔滨工业大学

出　　处：《哈尔滨师范大学自然科学学报》2004年第3期9-12,共4页Natural Science Journal of Harbin Normal University

摘　　要：本文对再生核空间W1 2 [a ,b]中的下面两个问题进行讨论 :( 1 )若再生核空间W1 2 [a ,b]定义中的条件改为u(x)在 [a ,b]是连续函数或连续囿变函数 ,那么函数空间不再是再生核空间 .( 2 )若再生核空间W W1 2 [a ,b]含有的间断点的函数 ,则间断点必固定、间断点个数必有限且非端点a ,b .进一步 。In a reproducing kernel space W 1 2 , the authors discuss two problems as follows:(1) If we replace the condition in the definition of a reproducing kernel space W 1 2 by the condition of u(x) being continuous or continuous and bounded variation, the function space would not be a reproducing kernel space. (2) If a reproducing kernel space WW 1 2 include discontinuous functions, the discontinuous points of functions must be immobile, the number be finite and not points of interval . Furthermore, we constructed a reproducing kernel space including functions with n-discontinuous points and give the expression of its reproducing kernel.

关 键 词：再生核空间 绝对连续函数 囿变函数 HIBERT空间 单调函数 

分 类 号：O174[理学—数学]