Some Properties of K-Frames in Hilbert Spaces

被引：105

作者：

Xiao, Xiangchun ^{[1
]}

Zhu, Yucan ^{[1
]}

Gavruta, Laura ^{[2
]}

机构：

[1] Fuzhou Univ, Dept Math & Comp Sci, Fuzhou 350002, Peoples R China

[2] Politehn Univ Timisoara, Dept Math, Timisoara 300006, Romania

来源：

RESULTS IN MATHEMATICS | 2013年 / 63卷 / 3-4期

关键词：

K-frame; ordinary frame; Bessel sequence;

D O I：

10.1007/s00025-012-0266-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

K-frames were recently introduced by GvruA a pound in Hilbert spaces to study atomic systems with respect to a bounded linear operator. From her discussions there are many differences between K-frames and ordinary frames, so in this paper we further discuss the interchangeability of two Bessel sequences with respect to a K-frame, where K is a bounded linear operator with closed range. We also give several methods to construct K-frames. In the end we discuss the stability of a more general perturbation for K-frame.

引用

页码：1243 / 1255

页数：13

共 18 条

[1]

[Anonymous], 2016, Appl. Numer. Harmon. Anal

[2]

[Anonymous], 2011, BULETINUL STIINTIFIC

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

Bolcskei, H ;

Hlawatsch, F ;

Feichtinger, HG .

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

[4]

Casazza P. G., 2004, CONTEMP MATH-SINGAP, V345, P87, DOI [10.1090/conm/345/06242, DOI 10.1090/conm/345/06242]

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

Casazza, Peter G. ;

Kutyniok, Gitta ;

Li, Shidong .

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

[6] Generalizing the Paley-Wiener perturbation theory for Banach spaces [J].

Casazza, PG ;

Kalton, NJ .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (02) :519-527

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

Cazassa, PG ;

Christensen, O .

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

[8] PAINLESS NONORTHOGONAL EXPANSIONS [J].

DAUBECHIES, I ;

GROSSMANN, A ;

MEYER, Y .

JOURNAL OF MATHEMATICAL PHYSICS, 1986, 27 (05) :1271-1283

[9] New perturbation results on pseudo-inverses of linear operators in Banach spaces [J].

Ding, J .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 362 :229-235

[10] A CLASS OF NONHARMONIC FOURIER SERIES [J].

DUFFIN, RJ ;

SCHAEFFER, AC .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 72 (MAR) :341-366

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