| Preface to first edition | p. v |
| Preface to second edition | p. ix |
| List of Figures | p. xvii |
| Orthogonal Series | p. 1 |
| General theory | p. 1 |
| Examples | p. 5 |
| Trigonometric system | p. 6 |
| Haar system | p. 10 |
| The Shannon system | p. 12 |
| Problems | p. 15 |
| A Primer on Tempered Distributions | p. 19 |
| Intuitive introduction | p. 20 |
| Test functions | p. 22 |
| Tempered distributions | p. 25 |
| Simple properties based on duality | p. 27 |
| Further properties | p. 29 |
| Fourier transforms | p. 30 |
| Periodic distributions | p. 32 |
| Analytic representations | p. 33 |
| Sobolev spaces | p. 35 |
| Problems | p. 35 |
| An Introduction to Orthogonal Wavelet Theory | p. 37 |
| Multiresolution analysis | p. 38 |
| Mother wavelet | p. 44 |
| Reproducing kernels and a moment condition | p. 53 |
| Regularity of wavelets as a moment condition | p. 55 |
| More on example 3 | p. 59 |
| Mallat's decomposition and reconstruction algorithm | p. 64 |
| Filters | p. 65 |
| Problems | p. 70 |
| Convergence and Summability of Fourier Series | p. 73 |
| Pointwise convergence | p. 73 |
| Summability | p. 79 |
| Gibbs phenomenon | p. 81 |
| Periodic distributions | p. 84 |
| Problems | p. 87 |
| Wavelets and Tempered Distributions | p. 91 |
| Multiresolution analysis of tempered distributions | p. 92 |
| Wavelets based on distributions | p. 95 |
| Distribution solutions of dilation equations | p. 95 |
| A partial distributional multiresolution analysis | p. 99 |
| Distributions with point support | p. 100 |
| Approximation with impulse trains | p. 104 |
| Problems | p. 107 |
| Orthogonal Polynomials | p. 109 |
| General theory | p. 109 |
| Classical orthogonal polynomials | p. 114 |
| Legendre polynomials | p. 115 |
| Jacobi polynomials | p. 119 |
| Laguerre polynomials | p. 120 |
| Hermite polynomials | p. 121 |
| Problems | p. 126 |
| Other Orthogonal Systems | p. 129 |
| Self adjoint eigenvalue problems on finite intervals | p. 130 |
| Hilbert-Schmidt integral operators | p. 132 |
| An anomaly: the prolate spheroidal functions | p. 134 |
| A lucky accident? | p. 135 |
| Rademacher functions | p. 140 |
| Walsh function | p. 142 |
| Periodic wavelets | p. 143 |
| Periodizing wavelets | p. 144 |
| Periodic wavelets from scratch | p. 146 |
| Local sine or cosine basis | p. 150 |
| Biorthogonal wavelets | p. 154 |
| Problems | p. 159 |
| Pointwise Convergence of Wavelet Expansions | p. 161 |
| Reproducing kernel delta sequences | p. 162 |
| Positive and quasi-positive delta sequences | p. 163 |
| Local convergence of distribution expansions | p. 169 |
| Convergence almost everywhere | p. 172 |
| Rate of convergence of the delta sequence | p. 173 |
| Other partial sums of the wavelet expansion | p. 177 |
| Gibbs phenomenon | p. 178 |
| Positive scaling functions | p. 181 |
| A general construction | p. 181 |
| Back to wavelets | p. 182 |
| Problems | p. 186 |
| A Shannon Sampling Theorem in Wavelet Subspaces | p. 187 |
| A Riesz basis of V[subscript m] | p. 188 |
| The sampling sequence in V[subscript m] | p. 189 |
| Examples of sampling theorems | p. 191 |
| The sampling sequence in T[subscript m] | p. 195 |
| Shifted sampling | p. 197 |
| Gibbs phenomenon for sampling series | p. 199 |
| The Shannon case revisited | p. 201 |
| Back to wavelets | p. 201 |
| Irregular sampling in wavelet subspaces | p. 212 |
| Problems | p. 214 |
| Extensions of Wavelet Sampling Theorems | p. 217 |
| Oversampling with scaling functions | p. 218 |
| Hybrid sampling series | p. 223 |
| Positive hybrid sampling | p. 225 |
| The convergence of the positive hybrid series | p. 228 |
| Cardinal scaling functions | p. 232 |
| Interpolating multiwavelets | p. 240 |
| Orthogonal finite element multiwavelets | p. 242 |
| Sobolev type norm | p. 244 |
| The mother multiwavelets | p. 245 |
| Problems | p. 252 |
| Translation and Dilation Invariance in Orthogonal Systems | p. 255 |
| Trigonometric system | p. 255 |
| Orthogonal polynomials | p. 256 |
| An example where everything works | p. 257 |
| An example where nothing works | p. 258 |
| Weak translation invariance | p. 259 |
| Dilations and other operations | p. 265 |
| Problems | p. 267 |
| Analytic Representations Via Orthogonal Series | p. 269 |
| Trigonometric series | p. 270 |
| Hermite series | p. 274 |
| Legendre polynomial series | p. 280 |
| Analytic and harmonic wavelets | p. 282 |
| Analytic solutions to dilation equations | p. 286 |
| Analytic representation of distributions by wavelets | p. 287 |
| Wavelets analytic in the entire complex plane | p. 291 |
| Problems | p. 293 |
| Orthogonal Series in Statistics | p. 295 |
| Fourier series density estimators | p. 296 |
| Hermite series density estimators | p. 299 |
| The histogram as a wavelet estimator | p. 301 |
| Smooth wavelet estimators of density | p. 305 |
| Local convergence | p. 309 |
| Positive density estimators based on characteristic functions | p. 310 |
| Positive estimators based on positive wavelets | p. 312 |
| Numerical experiment | p. 316 |
| Density estimation with noisy data | p. 318 |
| Other estimation with wavelets | p. 322 |
| Spectral density estimation | p. 322 |
| Regression estimators | p. 324 |
| Threshold Methods | p. 324 |
| Problems | p. 326 |
| Orthogonal Systems and Stochastic Processes | p. 329 |
| K-L expansions | p. 329 |
| Stationary processes and wavelets | p. 332 |
| A series with uncorrelated coefficients | p. 335 |
| Wavelets based on band limited processes | p. 341 |
| Nonstationary processes | p. 345 |
| Problems | p. 349 |
| Bibliography | p. 351 |
| Index | p. 363 |
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