关于W_2~1[a,b]能否扩大的一些问题

The Problem on Whether Reproducing Kernel SpaceW^1_2[a,b] Can be Expanded

讨论了W12[a,b]能否扩大为含有有间断点函数的再生核空间的问题.结论是:若再生核空间W W12[a,b]含有有间断点的函数,则间断点必固定、间断点个数必有限且非端点a,b.进一步,我们构造了函数含有n个间断点的再生核空间并给出其再生核表达式.

The authors discuss the problems whether a reproducing kernel space W^1_2[a,b] can be expanded into the space including discontinuous functions. We obtain the conclusions as follows. If a reproducing kernel space WW^1_2[a,b] include discontinuous functions, the discontinuous points of functions must be immobile, the number be finite and not points of interval [a,b]. Furthermore, we constructed a reproducing kernel space including functions with n-discontinuous points and give the expression of its reproducing kernel.