Weak (quasi-)affine bi-frames for reducing subspaces of L 2(a"e d )

被引：19

作者：

Jia HuiFang ^{[1
]}

Li YunZhang ^{[1
]}

机构：

[1] Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2015年 / 58卷 / 05期

基金：

北京市自然科学基金; 中国国家自然科学基金;

关键词：

frame; bi-frame; weak affine bi-frame; weak quasi-affine bi-frame; COMPACTLY SUPPORTED TIGHT; DUAL WAVELET FRAMES; MULTIRESOLUTION ANALYSIS; AFFINE SYSTEMS; CONSTRUCTION; L-2(R-D);

D O I：

10.1007/s11425-014-4906-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：1005 / 1022

页数：18

共 23 条

[1] Weak (quasi-)affine bi-frames for reducing subspaces of L2(ℝd)
HuiFang Jia
YunZhang Li
[J]. Science China Mathematics, 2015, 58 : 1005 - 1022
[2] Weak(quasi-)affine bi-frames for reducing subspaces of L~2(R~d)
JIA HuiFang
LI YunZhang
[J]. Science China Mathematics, 2015, 58 (05) : 1005 - 1022
[3] On a Class of Weak Nonhomogeneous Affine Bi-frames for Reducing Subspaces of L~2(R~d)
Jian Ping ZHANG
Yun Zhang LI
[J]. Acta Mathematica Sinica,English Series, 2017, (10) : 1339 - 1351
[4] On a class of weak nonhomogeneous affine bi-frames for reducing subspaces of L2(ℝd)
Jian Ping Zhang
Yun Zhang Li
[J]. Acta Mathematica Sinica, English Series, 2017, 33 : 1339 - 1351
[5] On a Class of Weak Nonhomogeneous Affine Bi-frames for Reducing Subspaces of L2 (Rd)
Zhang, Jian Ping
Li, Yun Zhang
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2017, 33 (10) : 1339 - 1351
[6] Weak Affine Super Bi-frames for Reducing Subspaces of L2(R, CL)
Li, Yun-Zhang
Tian, Yu
[J]. RESULTS IN MATHEMATICS, 2018, 73 (03)
[7] Refinable Function-Based Construction of Weak (Quasi-)Affine Bi-Frames
Jia, Hui-Fang
Li, Yun-Zhang
[J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2014, 20 (06) : 1145 - 1170
[8] Refinable Function-Based Construction of Weak (Quasi-)Affine Bi-Frames
Hui-Fang Jia
Yun-Zhang Li
[J]. Journal of Fourier Analysis and Applications, 2014, 20 : 1145 - 1170
[9] Weak Nonhomogeneous Wavelet Bi-Frames for Reducing Subspaces of Sobolev Spaces
Li, Yun-Zhang
Jia, Hui-Fang
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2017, 38 (02) : 181 - 204
[10] On the nonhomogeneous wavelet bi-frames for reducing subspaces of Hs(K)
Bhat, Mohammad Younus
[J]. ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES, 2022, 49 (02): : 401 - 410

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