PORTRAITS OF FRAMES

被引：94

作者：

ALDROUBI, A ^{[1
]}

机构：

[1] NIH,BIOMED ENGN & INSTRUMENTAT PROGRAM,NTTT,BETHESDA,MD 20894

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1995年 / 123卷 / 06期

关键词：

FRAMES; FRAME-PRESERVING MAPPINGS; AFFINE FRAMES; MULTIRESOLUTION; WAVELETS;

D O I：

10.2307/2160974

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce two methods for generating frames of a Hilbert space H. The first method uses bounded operators on H. The other method uses bounded linear operators on it to generate frames of H. We characterize all the mappings that transform frames into other frames. We also show how to construct all frames of a given Hilbert space H, starting from any given one. We illustrate the results by giving some examples from multiresolution and wavelet theory.

引用

页码：1661 / 1668

页数：8

共 17 条

[1] SAMPLING PROCEDURES IN FUNCTION-SPACES AND SYMPTOTIC EQUIVALENCE WITH SHANNON SAMPLING THEORY [J].

ALDROUBI, A ;

UNSER, M .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1994, 15 (1-2) :1-21

[2] DISCRETE SPLINE FILTERS FOR MULTIRESOLUTIONS AND WAVELETS OF L(2) [J].

ALDROUBI, A ;

EDEN, M ;

UNSER, M .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1994, 25 (05) :1412-1432

[3] FAMILIES OF MULTIRESOLUTION AND WAVELET SPACES WITH OPTIMAL PROPERTIES [J].

ALDROUBI, A ;

UNSER, M .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1993, 14 (5-6) :417-446

[4]

Aldroubi A, 1992, WAVELETS TUTORIAL TH, V1992, P509

[5]

Benedetto J. J., 1992, WAVELETS TUTORIAL TH, V2, P445

[6]

BENEDETTO JJ, 1993, ICASSP 93, V3, P304

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

DAUBECHIES, I .

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

[8]

Daubechies I., 1992, CBMS NSF REGIONAL C

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

DUFFIN, RJ ;

SCHAEFFER, AC .

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

[10] CONTINUOUS AND DISCRETE WAVELET TRANSFORMS [J].

HEIL, CE ;

WALNUT, DF .

SIAM REVIEW, 1989, 31 (04) :628-666

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