数学物理学报 ›› 2009, Vol. 29 ›› Issue (6): 1590-1600.

• 论文 • 上一篇    下一篇

若干周期再生核空间的覆盖数

  

  1. 绍兴文理学院数学系 浙江绍兴 312000
  • 收稿日期:2007-10-15 修回日期:2008-08-11 出版日期:2009-12-25 发布日期:2009-12-25
  • 基金资助:

    国家自然科学基金(10871226)资助

The |Covering Numbers for |Some Periodic Reproducing Kernel Spaces

  1. Department of Mathematics, Shaoxing College of Arts and Sciences, Zhejiang Shaoxing, 312000
  • Received:2007-10-15 Revised:2008-08-11 Online:2009-12-25 Published:2009-12-25
  • Supported by:

    国家自然科学基金(10871226)资助

摘要:

借助离散Fourier变换给出估计Mercer核矩阵逆矩阵范数上界的一种方法,由此给出了估计周期再生核Hilbert空间覆盖数的上、下界的一般方法.特别, 对两种特殊的周期再生核空间覆盖数的上、下界进行了比较.

关键词: 再生核Hilbert空间, 覆盖数, Fourier系数

Abstract:

A kind of method of estimating the norm of the inverse of the periodic Mercer kernel matrices is proposed with discrete Fourier transforms,with which a general way of estimating the upper and lower bounds of the covering
number for periodic reproducing kernel  Hilbert spaces is provided. In particular,the lower and upper bounds of the covering number for two special periodic  reproduced kernel spaces are compared.

Key words: Reproducing kernel Hilbert spaces, Covering numbers, Fourier coefficients

中图分类号: 

  • 68Q32