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| Авторизация |
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| Jorgensen P.E.T. — Analysis and Probability: Wavelets, Signals, Fractals |
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| Предметный указатель |
Fourier dual xxi xxx 35 60 81 198 207 209 210
Fourier equivalence 110
Fourier expansion xxii 61 157 158
Fourier frequency 21 26 69 70 110 255
Fourier pair xxi 36
Fourier series xxi xxii xxvii xxxi 10 32 59 67 69 80 145 163 206
Fourier transform xxi 4 10 35 102 105 111 114 191 208 257
Fourier variable 255 see
Fourier, inverse xxii
Fractal xxviii xxix xxxvi 7 15 21 22 34 35 37 67 72 74 77 80 97 152 182 194 198 210 211 227 231 254 255
Fractal analysis xxxv xliv 6 36 60 98 210
Fractal dimension see "dimension fractal"
Fractal Hilbert space see "space Hilbert fractal"
Fractal measure see "measure fractal"
Fractal theory xxix 25
Fractal wavelet see "wavelet fractal"
Fractal, affine see "affine fractal"
Fractions, 2-adic 89 138
Fractions, N-adic 90 92
Frame xliii 104 126 143 176 228—230
Frame bound 29 143 207 228
Frame constant see "frame bound"
Frame operator 207
Frame wavelet 100 229
Frame, affine wavelet 230
Frame, normalized tight 16 99 104 106 176 see Parseval"
Frame, Parseval 13 16 99 104—106 162 228
Frame, super- 230
Frame, tight 162 228
frequency xxxi xxxv 23 123 125 131 204 206 207 212 213 228
Frequency band xx 87 124 177 181 210
Frequency domain 4 87
Frequency response 4 17 87 131 204 206 207 210 227
Frequency subband 123
Frequency-localized wavelet see "wavelet frequency-localized"
Frobenius xliii see Perron Perron Perron Perron Perron
Fubini's theorem see "theorem Fubini's"
Function bounded measurable 43 47 49 51 53 61 115 219 253
Function filter 4 87 104 114 123 132 192 196 207 227 253
Function periodic 4 69 87 204 208 see l-periodic"
Function space see "space function"
Function theory xxviii xliv 46
Function,  - 13 14 111 190 210 251
Function, basis see "basis function"
Function, bounded continuous 14 195
Function, constant 15 46 61 91 136 256
Function, continuous 7 43 105 251
Function, eigen see "eigenfunction"
Function, father xxx 13 102 123—125 128 134 135
Function, filter response 87
Function, frequency response see "frequency response"
Function, generating 206
Function, harmonic see "harmonic function"
Function, indicator 14 52
Function, iterated — system see "iterated function system"
Function, l-periodic 18 60—62 66 95—97 104 132 174 175 217
Function, limit 50 54
Function, Lipschitz see "Lipschitz function"
Function, matrix 4 22 112 117 140 141 214 215
Function, matrix, unitary 227
Function, measurable xxxiv 7 47 54 60—62 65 70 84 87 115 199 252 255
Function, mother xxx 13 102 123—125 128 134 135
Function, multiplicity see "multiplicity function"
Function, operator 114 116 117
Function, operator, unitary xxix
Function, positive definite 57 203 204
Function, rational 34
Function, refinable 107
Function, scaling 3 see
Function, square-integrable 210 253
Function, step xxxi
Function, time-localized xxx 177
Function, vector-valued 131 210
Function, W- xxxiv 7 10 19 36 37 54 101 112
Function, wavelet see "wavelet function"
Function, zeta 34
G. Dirac 235
Gap-filling 14 see gap-filling"
Generalized multiresolution xxv 22 110 180 181 252
Generalized multiresolution analysis 109 114
GMRA see "generalized multiresolution grayscale" xviii 22 147 148 152 207 227
Gram Schmidt see "algorithm Gram
Group 1 5 28 36 70 109 110 205 210 211 214 221
Group, abelian 27 69
Group, abelian, compact 27
Group, Cantor 28
Group, circle 251 254
Group, cyclic 60 174 255
Group, infinite-dimensional unitary 155
Group, Lie 220
Group, non-abelian xxvi
Group, renormalization xxix
Group, sub- 230
Group, torus 204
Group, transformation 211
Haar measure see "measure Haar"
Haar wavelet see "wavelet Haar"
Harmonic analysis xix xxviii—xxx xliii 2 5 19 22 25 26 33 60 80 87 182 229
Harmonic function 9 18 21 22 43 48—52 55 76 86 91 92 95 100 252
Harmonic of iterated function systems xxx 14 67 80
Harmonic, boundary for 21 43 48 50
Harmonic, bounded 43 48—50
Harmonic, closed expression for 15 102 105
Harmonic, construction of 100
Harmonic, discrete 35
Harmonic, integral formula for 50
Harmonic, minimal 11 22 105
Hausdorff dimension see "dimension Hausdorff"
Hausdorff measure see "measure Hausdorff"
Hermitian operator see "operator hermitian"
High-pass filter see "filter high-pass"
Hilbert space see "space Hilbert"
Hutchinson measure see "measure Hutchinson"
I. Daubechies xxxii xxxiii 10 33 87
Image processing vi—viii xv xix xx xxii xxvi xxviii xxxii—xxxvii xliv 6 10 23 33 40 87 142 147 148 151 152 189 206 223—227 230 233 235 see
Infinite product xxviii—xxx 4 5 7 8 10—12 17—19 21 27 33—35 60 67 83—85 96 97 116 138 154 see infinite-product";
Infinite product, convergence of see "convergence of infinite product"
Infinite product, matrix 4 22
Infinite product, random 22 34
Infinite product, tensor 139 148 149 158
Infinite-dimensional unitary group see "group infinite-dimensional
Infinite-product measure see "measure infinite-product"
Integers 5 21 22 37 60 71 166 254 255
Integral translates 18 104 181
Intermediate differences 147 148
Intertwining 169 200 202 209
Interval, unit see "unit interval"
Invariant 51 52 66
Invariant measure see "measure invariant"
Invariant subspace 109 110 146 202 209 221
Invariant,  - 52 53
Invariant, R- 53
Invariant, shift- 51 52 92
Invariant, translation- 129
Irreducible representation see "representation irreducible"
Isometry xix 32 67 93—95 174 176 182—185 200 201 208 216 221 222 229 254
Isometry partial 94 150 173
Isomorphism 47 193 194 221
Isomorphism, *- 221
Isomorphism, C*-algebraic 139
Isomorphism, isometric 30 112 149 207
Isomorphism, order- 51
Isomorphism, unitary 162 169 191 193 194
Iterated function system xxx xxxv xliv 34 35 47 57 67 70 84 99 152 182 252 see
J. Cuntz xxii 183
J. Doob xxiv xxvi
J. Morlet xxxii
Jean Baptiste Joseph Fourier xxxi
Joint spectral radius xxxiii
JPEG 2000 xxxiii
| Karhunen-Lo'{e}ve decomposition theorem see "theorem Karhunen-Lo'{e}ve"
Kolmogorov consistency xxxi 7 45 46 48 49 141 203
Kolmogorov extension xxix 21 46 48 57 97 136 139 151
Kolmogorov's 0-1 law xxxiii 37
Kolmogorov's Lemma see "theorem "Kolmogorov's
Krieger - Cuntz algebra see "Cuntz-Krieger algebra"
L. Carleson 32
Lacunary trigonometric series 84
Lattice 4 154
Lattice operation 169 181 257
Lattice system see "statistical mechanics quantum"
Lattice, Bethe 98
Lattice, dual 28 36 69
Lebesgue measure see "measure Lebesgue"
Lebesgue's dominated convergence theorem see "theorem dominated
LIMIT 20 21 50 75 76 92 154 212
Limit function see "function limit"
Limit, inductive 139 140 252
Limit, martingale 49
Limit, non-tangential 50
Limit, Szego's — theorem see "theorem Szego's
Lipschitz continuous 77
Lipschitz function xxxiv 57 191
Lipschitz regularity see "regularity Lipschitz"
localization 22 158 see localized"; time-localized"; frequency-localized"
Localization of Mock Fourier series 80
Localization property of wavelet bases 80 87 157 225 226
Low-pass condition 17 228
Low-pass filter see "filter low-pass"
Low-pass property 125 130
M. Born 176 205 236
M. V. Wickerhauser 117 176 177
Mallat subdivision xxxi
Markov chain 50
Markov process 21
Markov transition measure see "measure transition"
Martingale xxix xxx xxxiii 10 21 35 36 50 51 57 91 168 255
Martingale convergence theorem see "theorem martingale
Martingale limit see "limit martingale"
Masking coefficient see "coefficient masking"
Mathematica 35
Mathematica, graphics produced using xxxiv xliii 2 123 125 129 152
Matrix 129 139 141 182 183 190 191 210 215 216 230 252 253
Matrix algebra see "algebra matrix"
Matrix algorithm see "algorithm matrix"
Matrix coefficient see "coefficient matrix"
Matrix diagonal 141
Matrix element 140 154
Matrix entry 219
Matrix factorization see "factorization matrix"
Matrix multiplication 25 128 142 143 202 210 216 230
Matrix operation 124
Matrix product xxvi 25 218 219 see matrix"
Matrix representation see "representation matrix"
Matrix step in algorithm xxxv 206 207 210
Matrix theory 34
Matrix wavelet 206 225
Matrix, adjoint 147 210 214
Matrix, diagonal 141
Matrix, function" see "function matrix"
Matrix, identity 183 252
Matrix, infinite — product see "infinite product matrix"
Matrix, infinite, xxvii 142 231
Matrix, integral 3
Matrix, operator 210 214 215 218
Matrix, Perron — Frobenius 34
Matrix, polyphase 205 210 215 218
Matrix, positive 34
Matrix, positive definite 203
Matrix, positive semidefinite 4
Matrix, propagator 34
Matrix, slanted 23—25 142 143 145 146 202 206 225 230 231
Matrix, sparse 23 206
Matrix, sub- 139
Matrix, Toeplitz 23 146
Matrix, unitary 109 129 174 182 191 201 205 210 211 214 216—218 220 221 227 see unitary matrix unitary"
Matrix-valued function see "function matrix"
Matrix-valued measure see "measure matrix-valued"
Matrix-valued wavelet filter see "wavelet filter matrix-valued"
Maximal abelian subalgebra 154 252
Measurable xxiv xxxiv 5 6 40 41 47 115 199 252 255
Measurable space xxxiv
Measurable,  - 41 53
Measurable, branch see "branch mapping measurable"
Measure xxiv xxvii 1 5 26 32 36 39 72 78 85 101 136 139—141 154 166 168 204 251 253—255 257
Measure extension 18 21 91 116 139 141 167 see
Measure space 6 40 84 94 115 139 149
Measure space, -finite 31 253
Measure theory viii 5 6 20 22 70 195 204
Measure, 53
Measure, -additive 115 167
Measure, absolutely continuous 50 136 154 257
Measure, atomic 100
Measure, Bernoulli—product see "measure p-Bernoulli—product"
Measure, Borel xxxiv 9 46 80 141 149 154
Measure, Cantor 12 14 74 198
Measure, determinantal 5 138 154 155
Measure, Dirac see "Dirac mass"
Measure, equivalent 154
Measure, Feynman 34
Measure, fractal xxiii 2 3 14 70 74 77
Measure, full 5 22 71 79
Measure, Haar xxvi 28 61 66 70 93 175 212 251 255
Measure, Hausdorff xxviii 2 14 17 72 74 97 176 196 198 199 251 252
Measure, Hausdorff, ambient 72
Measure, Hutchinson 48
Measure, infinite-product 149 154
Measure, invariant 52 53 70
Measure, Lebesgue xxviii 1 3 14 15 22 32 36 55 94 106 136 137 175 251
Measure, matrix-valued 111
Measure, non-atomic 41 91
Measure, operator-valued 114 115 117
Measure, orthogonal 167
Measure, p-Bernoulli—product 27
Measure, path-space xxviii xxx xxxi 1 4—9 11 18 19 21 26 34 35 37 43 45 51 57 59 60 65 70 71 77 79 84 91 98 100 111 115 122 130 254
Measure, Perron — Frobenius see "measure Perron
Measure, Perron — Frobenius — Ruelle 26 255
Measure, Poisson 50
Measure, positive xxxiv 4 36 44 46 51 115 141
Measure, probability xviii xxxiv 14 37 41 44 46 53 54 59 70 80 86 94 100 115 117 122 149 167 195 204
Measure, probability, Borel see "measure Borel"
Measure, probability, Radon see "measure Radon"
Measure, probability, s-fractal xxiii
Measure, product xxvii 91 149 157
Measure, projection-valued 112 135 136 142 166 167
Measure, Radon 43 44 46 49 85 86 115—117 122
Measure, Ruelle see "measure Perron
Measure, spectral 112
Measure, transition xxxiv 21 90
Measure, W- xxxiv 9 26
Middle-third Cantor Set see "Cantor set middle-third"
Minimal 11 171 172
Minimal eigenfunction see "eigenfunction minimal"
Mirror 33 212 228
Mirror, quadrature see "filter quadrature-mirror"
Mock Fourier series 80
Monotonicity 92 155
Mother function see "function mother"
MRA see "multiresolution analysis"
Multiindex 165—167 252
Multiplicity 111
Multiplicity function 114 117 255
Multiresolution xviii—xx xxvi xxxi xxxii 9 10 35 36 59 110 114 153 168—171 179 187 189 198 222 223 see multiresolution"
Multiresolution analysis 6 16 36 109 181 194 198 252 253
Multiresolution wavelet see "wavelet multiresolution"
Multiresolution, orthogonal 172
Multiwavelet 5 7 111 114 116 153
N-adic 126
N-adic map 90
N-adic rationale 92
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