LIST O F FIGURE S Figure 1.1.1 Poisson kernel Pr(0) with r = 0.8 [Page 8] Figure 1.1.2 Conjugate Poisson kernel Qr(0) with r = 0.8 [Page 9] Figure 1.2.1 The Dirichlet kernel DN (u) with N = 5 [Page 16] Figure 1.2.2 Graphs of the partial sums SNf(x) foxN= 1, 2, 3 of the Fourier series of f(x) = JC, —ft x Tt [Page 16] Figure 1.2.3 The Gibbs-Wilbraham phenomenon for the function f(x) — sgn(x) [Page 35] Figure 1.4.1 Relations between Abel and Cesaro summability. Stronger methods are to the right of weaker methods [Page 53] Figure 1.4.2 The Fejer kernel with T V = 8 [Page 56] Figure 1.5.1 The de la Vallee Poussin kernel with N = & [Page 69] Figure 2.5.1 The spherical partial sum of the indicator function of the unit ball in R3, with M = 99 fin [Page 144] Figure 2.5.2 Illustrating Huygens' principle [Page 149] Figure 6.1.1 Gaussian wavelet [Page 289] Figure 6.1.2 Mexican hat wavelet [Page 289]

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