Wavelets: Theory and Applications

Index

admissibility condition, 2

admissible function, 45, 53

admissible vector, 40

analysis of an electrocardiogram, 232

anisotropy, 119

anisotropy values, 237, 239

approximate inverse, 257

approximation property of wavelets, 254

inverse, 255

Aubin–Nitsche trick, 263

basis function, 119

Battle–Lemarié wavelet, 132, 135

bilinear form

H₀¹ In-elliptic, 261

continuous, 261

boundary layers, 278, 304

boundary measure, 300

numerical, 301

boundary value problem, 260

B-spline, 62, 132, 148

Calderón’s formula, 9

Cauchy inequality

strengthened, 286

CG method, 302

preconditioned, 304

Cohen’s criterion, 139, 209

coifiets, 202

compression rate, 240

computerized tomography, 251

condition of a matrix, 273

congruent set, 138

connection coefficients, 281, 285, 290, 297, 298

convolution theorem, 12, 310

Daubechies scaling function, 160, 287

Daubechies wavelet, 159, 161, 162, 164, 165, 168, 175, 223, 233, 277

induced, 210

order of a, 164, 165, 168

decay behaviour

of the wavelet transform, 32–34, 65, 67

dilation matrix, 117, 119, 120

embedding theorem

Sobolev’s, 312

entropy of a sequence, 244

exponent

critical, 171

  of the Daubechies wavelet, 173

Hölder, 170

  of the Daubechies wavelet, 175

fibre space, 59

fictitious domain, 300, 303, 304

fictitious domain method, 300

filter

band pass, 12, 13, 20, 169

conjugate quadrature, 156

high pass, 12

linear convolution, 12

low pass, 12, 20, 102, 169

Fourier transform, 2, 51, 309–311

inverse, 309

windowed, 16, 20, 41, 48

frame, 94, 95, 97

tight, 74,