Title | Advances in Gabor Analysis [electronic resource] / edited by Hans G. Feichtinger, Thomas Strohmer |
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Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2003 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0133-5 |
Descript | XIX, 356 p. online resource |
1 Introduction -- 1.1 Recent Trends in Gabor Analysis -- 1.2 Outline of the Book -- 2 Uncertainty Principles for Time-Frequency Representations -- 2.1 Introduction -- 2.2 The Classical Uncertainty Principle -- 2.3 Time-Frequency Representations -- 2.4 Support Conditions -- 2.5 Essential Support Conditions -- 2.6 Hardyโs Uncertainty Principle -- 2.7 Beurlingโs Theorem -- References -- 3 Zak Transforms with Few Zeros and the Tie -- 3.1 Introduction and Announcements of Results -- 3.2 Zak Transforms with Few Zeros -- 3.3 When is (?[0, c0),a, b) a Gabor Frame? โ -- References -- 4 Bracket Products for Weyl-Heisenberg Frames -- 4.1 Introduction -- 4.2 Preliminaries -- 4.3 Pointwise Inner Products -- 4.4 a-Orthogonality -- 4.5 a-Factorable Operators -- 4.6 WeylโHeisenberg Frames and the a-Inner Product -- References -- 5 A First Survey of Gabor Multipliers -- 5.1 Introduction -- 5.2 Notation and Conventions -- 5.3 Basic Theory of Gabor Multipliers -- 5.4 From Upper Symbol to Operator Ideal -- 5.5 Eigenvalue Behavior of Gabor Multipliers -- 5.6 Changing the Ingredients -- 5.7 From Gabor Multipliers to their Upper Symbol -- 5.8 Best Approximation by Gabor Multipliers -- 5.9 STFT-multipliers and Gabor Multipliers -- 5.10 Compactness in Function Spaces -- 5.11 Gabor Multipliers and Time-Varying Filters -- References -- 6 Aspects of Gabor Analysis and Operator Algebras -- 6.1 Introduction -- 6.2 Background -- 6.3 The Density (or Incompleteness) Property -- 6.4 Characterizing the Unique Gabor Dual Property -- 6.5 Gabor Frames for Subspaces -- References -- 7 Integral Operators, Pseudo differential Operators,and Gabor Frames -- 7.1 Introduction -- 7.2 Discussion and Statement of Results -- 7.3 The Modulation Spaces -- 7.4 Invariance Properties of the Modulation Space -- 7.5 Gabor Frames -- 7.6 An Easy Trace-Class Result -- 7.7 Finite-Rank Approximations -- 7.8 Improving the Estimate -- 7.9 Conclusion and Observations -- References -- 8 Methods for Approximation of the Inverse (Gabor) Frame Operator -- 8.1 Introduction -- 8.2 The Double Projection Method -- 8.3 Projection Methods for Gabor Frames -- 8.4 On Sampling of Gabor Frames in L2(?) -- References -- 9 Wilson Bases on the Interval -- 9.1 Introduction -- 9.2 Wilson Bases of L2(?) -- 9.3 Wilson Bases for Periodic Functions -- 9.4 Wilson Bases on the Interval -- 9.5 Algorithms -- References -- 10 Localization Properties and Wavelet-Like Orthonormal Bases for the Lowest Landau Level -- 10.1 Introduction: Phase Space Localization -- 10.2 The Fractional Quantum Hall Effect -- 10.3 A Toy Model -- 10.4 Wavelet Bases for the LLL -- 10.5 Magnetic Translations and Multiresolution Analysis -- 10.6 Conclusion -- 10.7 Appendix: Two Mathematical Tools -- References -- 11 Optimal Stochastic Encoding and Approximation Schemes using WeylโHeisenberg Sets -- 11.1 Introduction -- 11.2 Stochastic Processes and Statement of the Problems -- 11.3 Semi-optimal and Optimal Solutions -- 11.4 Non-Localization Results -- 11.5 Numerical Examples -- 11.6 Conclusions -- References -- 12 Orthogonal Frequency Division Multiplexing Based on Offset QAM -- 12.1 Introduction and Outline -- 12.2 Orthogonal Frequency Division Multiplexing Based on OQAM -- 12.3 Orthogonality Conditions for OFDM/OQAM Pulse Shaping Filters -- 12.4 Design of OFDM/OQAM Filters -- 12.5 Biorthogonal Frequency Division Multiplexing Based on Offset QAM -- 12.6 Conclusion -- 12.7 Appendix -- References