Applications of Parameterizations of Oblique Duals of a Frame Sequence

被引：8

作者：

Kim, Hyoungseok ^{[1
]}

Koo, Yoo Young ^{[2
]}

Lim, Jae Kun ^{[3
]}

机构：

[1] Dong Eui Univ, Dept Multimedia Engn, Pusan, South Korea

[2] Yonsei Univ, Univ Coll, Seoul 120749, South Korea

[3] Hankyong Natl Univ, Dept Appl Math, Gyeonggido 456749, South Korea

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2013年 / 34卷 / 08期

关键词：

Deficit; Dual; Excess; Frame; Frame sequence; Oblique dual; Rank; Type I dual; Type II dual; HILBERT-SPACE; RIESZ BASES; OPERATORS;

D O I：

10.1080/01630563.2013.806545

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Two parameterizations of oblique duals of a given frame sequence are applied to show that the sum of a frame sequence and one of its oblique duals may not be a frame sequence, and that type II dual is locally (and globally) optimal in some sense and that the excesses of the frame sequence and its oblique duals are the same. Other observations on the duals of a frame sequence are included also.

引用

页码：896 / 913

页数：18

共 21 条

[1]

Andruchow Esteban, 2008, Sampling Theory in Signal and Image Processing, V7, P313

[2] Invariances of frame sequences under perturbations [J].

Bishop, Shannon ;

Heil, Christopher ;

Koo, Yoo Young ;

Lim, Jae Kun .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (06) :1501-1514

[3] The art of frame theory [J].

Casazza, PG .

TAIWANESE JOURNAL OF MATHEMATICS, 2000, 4 (02) :129-201

[4] FRAMES AND PSEUDO-INVERSES [J].

CHRISTENSEN, O .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 195 (02) :401-414

[5] Oblique dual frames and shift-invariant spaces [J].

Christensen, O ;

Eldar, YC .

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2004, 17 (01) :48-68

[6]

Conway J. B., 1990, COURSE FUNCTIONAL AN

[7]

DEUTSCH F, 1995, NATO ADV SCI INST SE, V454, P107

[8] ON MAJORIZATION FACTORIZATION AND RANGE INCLUSION OF OPERATORS ON HILBERT SPACE [J].

DOUGLAS, RG .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 17 (02) :413-&

[9] OPERATOR RANGES [J].

FILLMORE, PA ;

WILLIAMS, JP .

ADVANCES IN MATHEMATICS, 1971, 7 (03) :254-&

[10]

Groetsch Charles W., 1977, Generalized inverses of linear operators

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