On characterization and stability of alternate dual of g-frames

被引：19

作者：

Arefijamaal, Ali Akbar ^{[1
]}

Ghasemi, Soheila ^{[1
]}

机构：

[1] Sabzevar Tarbiat Moallem Univ, Dept Math & Comp Sci, Sabzevar, Iran

来源：

TURKISH JOURNAL OF MATHEMATICS | 2013年 / 37卷 / 01期

关键词：

Frame; dual frame; g-Riesz sequence; alternate dual; g-frame;

D O I：

10.3906/mat-1107-14

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

One of the essential applications of frames is that they lead to expansions of vectors in the underlying Hilbert space in terms of the frame elements. In this decomposition, dual frames have a key role. G-frames, introduced by Sun, cover many other recent generalizations of frames. In this paper, we give some characterizations of dual g-frames. Moreover, we prove that if two g-frames are close to each other, then we can find duals of them which are close to each other.

引用

页码：71 / 79

页数：9

共 22 条

[1] Some results on g-frames in Hilbert spaces [J].

Abdollahi, Abdolaziz ;

Rahimi, Elham .

TURKISH JOURNAL OF MATHEMATICS, 2011, 35 (04) :695-704

[2] CONTINUOUS FRAMES IN HILBERT-SPACE [J].

ALI, ST ;

ANTOINE, JP ;

GAZEAU, JP .

ANNALS OF PHYSICS, 1993, 222 (01) :1-37

[3] Generalized frames and their redundancy [J].

Askari-Hemmat, A ;

Dehghan, MA ;

Radjabalipour, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (04) :1143-1147

[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] Frame-theoretic analysis of oversampled filter banks [J].

Bolcskei, H ;

Hlawatsch, F ;

Feichtinger, HG .

IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1998, 46 (12) :3256-3268

[6] New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities [J].

Candès, EJ ;

Donoho, DL .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2004, 57 (02) :219-266

[7] Fusion frames and distributed processing [J].

Casazza, Peter G. ;

Kutyniok, Gitta ;

Li, Shidong .

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2008, 25 (01) :114-132

[8] Perturbation of operators and applications to frame theory [J].

Cazassa, PG ;

Christensen, O .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 1997, 3 (05) :543-557

[9]

Christensen O, 2008, APPL NUMER HARMON AN, P1, DOI 10.1007/978-0-8176-4678-3_1

[10] THE WAVELET TRANSFORM, TIME-FREQUENCY LOCALIZATION AND SIGNAL ANALYSIS [J].

DAUBECHIES, I .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1990, 36 (05) :961-1005

← 1 2 3 →