Positive Weight Function and Classification of g-Frames

被引：0
作者：
Poria, Anirudha [1 ,2 ]
机构：
[1] Indian Inst Sci, Dept Math, Bengaluru, Karnataka, India
[2] Bennett Univ, Dept Math, Sch Engn & Appl Sci, Greater Noida, Uttar Pradesh, India
来源：
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2020年 / 41卷 / 08期
关键词：
g-frames; g-Riesz bases; Heisenberg group; shift-invariant subspaces; weight function; SUBSPACES; WAVELETS; SPACES; L-2;
D O I：
10.1080/01630563.2020.1728771
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Given a positive weight function and an isometry map on a Hilbert spaces we study a class of linear maps which is a g-frame, g-Riesz basis, and a g-orthonormal basis for with respect to in terms of the weight function. We apply our results to study the frame for shift-invariant subspaces on the Heisenberg group.
引用
收藏
页码：950 / 968
页数：19
相关论文
共 21 条
[1]   Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2 (Rd) [J].
Aldroubi, A ;
Cabrelli, C ;
Molter, UM .
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2004, 17 (02) :119-140
[2]  
[Anonymous], 1994, Wavelets: Mathematics and Applications
[3]   Bracket map for the Heisenberg group and the characterization of cyclic subspaces [J].
Barbieri, Davide ;
Hernandez, Eugenio ;
Mayeli, Azita .
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2014, 37 (02) :218-234
[4]   Sigma-Delta (ΣΔ) quantization and finite frames [J].
Benedetto, JJ ;
Powell, AM ;
Yilmaz, Ö .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (05) :1990-2005
[5]   Continuous Curvelet Transform -: II.: Discretization and frames [J].
Candès, EJ ;
Donoho, DL .
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2005, 19 (02) :198-222
[6]   Harmonic analysis of neural networks [J].
Candès, EJ .
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 1999, 6 (02) :197-218
[7]  
Casazza P. G., 2004, CONTEMP MATH-SINGAP, V345, P87, DOI [10.1090/conm/345/06242, DOI 10.1090/conm/345/06242]
[8]   Oblique dual frames and shift-invariant spaces [J].
Christensen, O ;
Eldar, YC .
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2004, 17 (01) :48-68
[9]  
Dörfler M, 2006, MATH SCAND, V98, P81
[10]   A CLASS OF NONHARMONIC FOURIER SERIES [J].
DUFFIN, RJ ;
SCHAEFFER, AC .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 72 (MAR) :341-366
123