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Fourier Series and Wavelets. Vol 2

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Fourier Series and Wavelets. Vol 2

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Mục lục

  • PART II. - WAVELETS

    • Chapter 0. - A brief historical account

      • 1. Jean Morlet and the beginning of wavelet theory (1982)

      • 2. Alex Grossmann and the Marseille team (1984)

      • 3. Yves Meyer and the triumph of harmonie analysis (1985)

      • 4. Stéphane Mallat and the fast wavelet transform (1986)

      • 5. Ingrid Daubechies and the FIR filters (1987)

      • Chapter 1. - The notion of wavelet representation

        • 1. Time-frequency localization and Heisenberg's inequality

        • 2. Almost orthogonal families, frames and bases in a Hilbert space

        • 3. Fourier Windows, Gabor wavelets and the Balian-Low theorem

        • 5. Wavelet analysis of global regularity

        • 6. Wavelet analysis of pointwise regularity

        • Chapter 2. - Discrete wavelet transforms

          • 1. Sampling theorems for the Morlet wavelet representation

          • 2. The vaguelettes lemma and related results for the Hε,ε' spaces

          • 3. Proof of the regular sampling theorem

          • 4. Proof of the irregular sampling theorem

          • 5. Some remarks on dual frames

          • 6. Wavelet theory and modem Littlewood-Paley theory

          • Chapter 3. - The structure of a wavelet basis

            • 1. General properties of shift-invariant spaces

            • 2. The structure of a wavelet basis

            • 3. Definition and examples of multi-resolution analysis

            • 4. Non-existence of regular wavelets for the Hardy space H2

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