高维Sobolev空间中的小波级数  

Wavelet Expansion of High-dimensional Sobolev Space

作　　者：赵书改[1] 

机构地区：[1]咸阳师范学院数学与信息科学学院,陕西咸阳712000

出　　处：《河南科学》2015年第2期157-159,共3页Henan Science

基　　金：陕西省科技厅科技发展计划项目(2013JM1014)

摘　　要：研究高维空间中小波级数的收敛性与收敛速度.通过对小波级数余项的研究,利用逼近论的思想和Parseval不等式探索高维Sobolev空间中小波级数的余项,建立小波级数的余项的估计,进而得到小波级数一致收敛的结论和一致收敛速度的精确估计.Convergence and convergence rate of wavelet expansion of high-dimensional Sobolev space are researched in this paper. Based on the study of the remainder of the wavelet expansion, methods of approximating and Parseval inequality are used to explore the remainder of wavelet expansion, and the estimation of the remainder is established. Then result of uniform convergence of wavelet expansion and exact estimation of uniform convergence rate are obtained.

关 键 词：SOBOLEV空间 小波级数 收敛性 Schwartz类 

分 类 号：O177.1[理学—数学]