Weak(quasi-)affine bi-frames for reducing subspaces of L^2(R^d)

作     者：JIA HuiFang LI YunZhang 

作者机构：College of Applied Sciences Beijing University of Technology 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2015年第58卷第5期

页      面：1005-1022页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.11271037) Beijing Natural Science Foundation(Grant No.1122008) 

主　　题：frame bi-frame weak affine bi-frame weak quasi-affine bi-frame 

摘      要：Since a frame for a Hilbert space must be a Bessel sequence, many results on(quasi-)affine bi-frame are established under the premise that the corresponding(quasi-)affine systems are Bessel sequences. However,it is very technical to construct a(quasi-)affine Bessel sequence. Motivated by this observation, in this paper we introduce the notion of weak(quasi-)affine bi-frame(W(Q)ABF) in a general reducing subspace for which the Bessel sequence hypothesis is not needed. We obtain a characterization of WABF, and prove the equivalence between WABF and WQABF under a mild condition. This characterization is used to recover some related known results in the literature.