Wavelet Analysis

Chapter 1. Introduction. Chapter 2. Wavelets on Euclidean Spaces. 2.1. Introduction. 2.2. Wavelets on R. 2.3. Multi-Resolution Analysis. 2.4. Wavelet Algorithms. 2.5. Wavelet Basis. 2.6. Multidimensional Real Wavelets. 2.7. Examples of Wavelet Functions and MRA. 2.8. Exercise. 3. Wavelets Extended. 3.1. Affine Group Wavelets. 3.2. Multiresolution Analysis on The Interval. 3.3 Wavelets on The Sphere. 3.4. Exercise. 4. Clifford Wavelets. 4.1. Introduction. 4.2. Different Constructions of Clifford Algebra. 4.3. Graduation in Clifford Algebra. 4.4. Some useful operations of Clifford Algebra. 4.5. Clifford Functional Analysis. 4.6. Existence of Monogenic Extensions. 4.7. Clifford-Fourier Transform. 4.8. Some Experimentations. 4.9. Exercise. 5. Quantum Wavelets. 5.1. Introduction. 5.2. Bessel Functions. 5.3. Bessel Wavelets. 5.4. Fractional Bessel Wavelets. 5.5. Quantum Theory Toolkit. 5.6. Some Quantum Special Functions. 5.7. Quantum Wavelets. 5.8. Exercise. 6. Wavelets in Statistics. 6.1 Introduction. 6.2. Wavelet Analysis of Time Series. 6.3. Wavelet Variance and Covariance. 6.4. Wavelet Decimated and Stationary Transforms. 6.5. Wavelet Density Estimation. 6.6. Wavelet Thresholding. 6.7. Application to Wavelet Density Estimations. 6.8. Exercise. 7. Wavelets for Partial Differential Equations. 7.1. Introduction. 7.2. Wavelet Collocation Method. 7.3. Wavelet Galerkin Approach. 7.4. Reduction of the Connection Coefficients Number. 7.5. Two Main Applications for Solving PDEs. 7.6. Appendix. 7.7. Exercise. 8. Wavelets for Fractal and Multifractal Functions. 8.1. Introduction. 8.2. Hausdorff Measure and Dimension. 8.3. Wavelets for The Regularity Of Functions. 8.4. The Multifractal Formalism. 8.5. Similar Type Functions. 8.6. Application to Financial Index Modeling. 8.7. Appendix. 8.8. Exercise.