the Fourier transform to solve ordinary and partial differential equations
6.12. Summary
13 Appendix 2: The Transpose (or Dual) of a Linear Operator
14 Appendix 3: Uniform, Strong and Weak Convergence
15 References
16 Index
Guide
1 Cover
6 Preface
8 Index
List of Illustrations
1 Chapter 1Figure 1.1. Parallelogram law in ℝ2: The sum of the squares of the two diagonal ...Figure 1.2. Orthogonal projection and diagonal projections and of a vector in...Figure 1.3. Visualization of property 2 in ℝ2. For a color version of this figur...Figure 1.4. Orthogonal projection p of a vector in ℝ3 onto the plane produced by...Figure 1.5. Illustration of the second step in the Gram-Schmidt orthonormalizati...
2 Chapter 2Figure 2.1. Hm for m = 1, N = 16Figure 2.2. Hm for m = 2, N = 16Figure 2.3. Filtering approach in the Fourier domainFigure 2.4. Difference between the sine functions representing the spectrum valu...Figure 2.5. The two coordinates of a pixel, n1 n2, in a digital image (image sou...Figure 2.6. a) Original image of Panko; b) image after Laplacian filter; c) imag...Figure 2.7. Left column: original images. Right column: centered amplitude spect...Figure 2.8. Two-dimensional Gaussian images with a standard deviation of (left -...Figure 2.9. Blurred image of Lena obtained by multiplying DFTs and Gaussians wit...Figure 2.10. Blurring filter/low-pass filter in the frequency domain
3 Chapter 3Figure 3.1. Riemann and Lebesgue integration. For a color version of this figure...
4 Chapter 5Figure 5.1. Two-dimensional geometric visualization of the property verified by ...Figure 5.2. Gibbs phenomenon for the rectangular pulse function (courtesy of Éri...
5 Chapter 6Figure 6.1. The line of equation (shown in blue) is the best approximation of t...
List of Tables
1 Chapter 2Table 2.1. Different normalizations of Fourier bases and relative formulasTable 2.2. Fourier pairs and translationTable 2.3. Fourier pairs relative to convolutionTable 2.4. Fourier pair for the convolution between a signal z and the unit puls...Table 2.5. Fourier pairs for 2D shifts
2 Chapter 5Table 5.1. Analogies between a finite-dimensional Euclidean space and an infinit...
3 Chapter 6Table 6.1. Properties of the Fourier transform on S(ℝ)Table 6.2. Properties of the Fourier transform on S(ℝn)
Pages
1 v
2 ii
3 iii
4 iv
5 xi
6 xii
7 1
8 2
9 3
10 4
11 5
12 6
13 7
14 8
15 9
16 10
17 11
18
