Advances in Gabor Analysis
Springer-Verlag New York Inc.
978-1-4612-6627-3 (ISBN)
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 Hardy’s Uncertainty Principle.- 2.7 Beurling’s 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? “.- 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 Weyl—Heisenberg 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 Weyl—Heisenberg 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.
Reihe/Serie | Applied and Numerical Harmonic Analysis |
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Zusatzinfo | XIX, 356 p. |
Verlagsort | New York |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik |
Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika | |
Mathematik / Informatik ► Mathematik ► Analysis | |
Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
Technik ► Elektrotechnik / Energietechnik | |
Schlagworte | Analysis |
ISBN-10 | 1-4612-6627-0 / 1461266270 |
ISBN-13 | 978-1-4612-6627-3 / 9781461266273 |
Zustand | Neuware |
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