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PRINTED BOOKS
Author Kutyniok, Gitta.

Title Affine density in wavelet analysis / Gitta Kutyniok.

Published Berlin ; New York : Springer, [2007]
©2007

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Location Call No. Status
 UniM ERC  510 LECT  no. 1914    AVAILABLE
Physical description xii, 138 pages ; 24 cm.
Series Lecture notes in mathematics, 0075-8434 ; 1914.
Lecture notes in mathematics (Springer-Verlag) ; 1914.
Bibliography Includes bibliographical references (pages [127]-133) and index.
Contents 1.1 Irregular Wavelet and Gabor Frames 1 -- 1.2 Density for Gabor Systems 3 -- 1.3 Geometry of Time-Scale Indices 5 -- 1.4 Overview of Main Results 7 -- 2 Wavelet and Gabor Frames 11 -- 2.1 Frame Theory 11 -- 2.2 Wavelet Analysis 13 -- 2.3 Time-Frequency Analysis 16 -- 2.4 Amalgam Spaces 19 -- 3 Weighted Affine Density 21 -- 3.2 Basic Properties 24 -- 3.3 Notion of Affine Density by Sun and Zhou 27 -- 3.4 Comparison of Both Notions of Affine Density 32 -- 4 Qualitative Density Conditions 35 -- 4.1 Existence of an Upper Frame Bound 35 -- 4.2 Existence of a Lower Frame Bound 37 -- 4.3 Examples of Wavelet Systems 42 -- 4.4 Density of Sequences in R+ 45 -- 4.5 Affine Density and the Local Integrability Condition 48 -- 5 Quantitative Density Conditions 59 -- 5.1 Outline and Comparison with Previous Work 59 -- 5.2 Density of Product Sequences 61 -- 5.3 A Fundamental Relationship 63 -- 5.4 Nyquist Phenomenon 75 -- 5.5 Sufficient Density Conditions for Wavelet Frames 76 -- 5.6 Existence of Special Weight Functions 81 -- 5.7 Co-Affine Systems 82 -- 6 Homogeneous Approximation Property 87 -- 6.1 Amalgam Spaces and the Continuous Wavelet Transform 87 -- 6.2 Basic Class B[subscript 0] 89 -- 6.3 Homogeneous Approximation Property for Wavelet Frames 93 -- 6.4 Comparison Theorem for Wavelet Frames 97 -- 6.5 Density Results for Wavelet Schauder Bases 100 -- 7 Weighted Beurling Density and Shift-Invariant Gabor Systems 105 -- 7.1 Motivation and Outline of Chapter 105 -- 7.2 Weighted Beurling Density 107 -- 7.3 Littlewood-Paley Type Inequalities 110 -- 7.4 Equivalent Definition of Weighted Beurling Density 115 -- 7.5 Beurling Density, Frame Bounds, and Gabor Generators 119 -- 7.6 Shift-Invariant Gabor Systems 121.
Subject Wavelets (Mathematics)
ISBN 9783540729167
354072916X