On a Class of Weak Nonhomogeneous Affine Bi-frames for Reducing Subspaces of L^2(R^d)  

作　　者：Jian Ping ZHANG Yun Zhang LI 

机构地区：[1]College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2017年第10期1339-1351,共13页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11271037)

摘　　要：For refinable functiombased affine bi-frames, nonhomogeneous ones admit fast algorithms and have extension principles as homogeneous ones. But all extension principles are based on some restrictions on refinable functions. So it is natural to ask what are expected from general refinable functions. In this paper, we introduce the notion of weak nonhomogeneous affine bi-frame （WNABF）. Under the setting of reducing subspaces of L2（Rd）, we characterize WNABFs and obtain a mixed oblique extension principle for WNABFs based on general refinable functions.For refinable functiombased affine bi-frames, nonhomogeneous ones admit fast algorithms and have extension principles as homogeneous ones. But all extension principles are based on some restrictions on refinable functions. So it is natural to ask what are expected from general refinable functions. In this paper, we introduce the notion of weak nonhomogeneous affine bi-frame （WNABF）. Under the setting of reducing subspaces of L2（Rd）, we characterize WNABFs and obtain a mixed oblique extension principle for WNABFs based on general refinable functions.

关 键 词：FRAME reducing subspace weak affine bi-frame weak nonhomogeneous affine bi-frame extension principle 

分 类 号：O177.1[理学—数学]