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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 |
N-adic subinterval 47
n-fold branch mapping see "branch mapping n-fold"
N. Wiener 34
Natural numbers xviii 5 21 40 52 66 71 85 167 254
Nikodym, Radon derivative see "derivative Radon
Non-abelian see "algebra non-abelian"; non-abelian"
Non-atomic see "measure non-atomic"
Non-commutative setting xv xxvi xxix 5 7 37 58 115 139 151 177 234 see non-commutative"
Non-overlapping 187 199
Non-overlapping partition see "partition non-overlapping"
Norm xviii 12 14 17 31 44 48 139 168 173 181 204 210 228
Normalization 12 14 15 37 53 54 61 64 70 101 114 125 127 135
Normalized solution 12 14
Notational convention 17 204
O. Heaviside xvi 157 223 235
ONB see "basis orthonormal"
One-torus 60 251 254
Operator 132 140 141 158 160 162 172 192 196 210—212 215 216 219 254
Operator algebra xxviii—xxx xxxvi 6 22 37 138 154 155 205 210 211 216 218
Operator coefficient see "coefficient operator"
Operator factorization see "factorization operator"
operator function see "function operator"
Operator matrix see "matrix operator"
Operator monomial 165
Operator process 116
Operator product 115 218
Operator theory xix xxvi xxix 10 37 58 109 138 142 154 170 180 181 186 210—212 216 221 222 229 230
Operator, adjoint 93 144 145 147 157 160 165 185 200 209 210 212—214 216 217 254
Operator, bounded 218
Operator, bounded linear 218 251
Operator, compact 55 58
Operator, conjugation see "conjugation"
Operator, filter 135
Operator, filter ,subband- 213
Operator, frame see "frame operator"
Operator, hermitian 209
Operator, Hilbert space see "space Hilbert operators"
Operator, identity 131 136 174 182 209 252 256
Operator, linear 140
Operator, multi- 165
Operator, multiplication 94 95 110 142 147 198 209 210 213 217 221 253
Operator, non-commuting see "non-commutative setting"
Operator, Perron — Frobenius — Ruelle xxxiv xliv 4 8 9 19 21 26 33 43 48 49 57 61 86 87 95 97 107 155 200 254
Operator, positive 117 254
Operator, positive semidefinite 114
Operator, projection see "projection
Operator, row" 210
Operator, scaling xx 2 3 10 109 162 180 181 187 188 190 200 207—209 255
Operator, scaling, unitary 163 168 194 196
Operator, selfadjoint 138
Operator, semidefinite 114
Operator, shift 213 256
Operator, transfer xxxiii xliii xliv 4 19 26 33—35 57 87 115 254 see Perron
Operator, transfer wavelet xxxiii 33 105 107
Operator, transition xxxiv 8 9 21 see Perron
Operator, transition wavelet, xxxiv 21
Operator, unitary xix 158 161 169 179—183 186 188—190 210 211 218 219 221 see operator unitary"
Operator, unitary valued measure see "measure operator-valued"
Operator, zero-kernel 116
Ordering 51 209
Orthogona vectors 181 190
Orthogonal 198
Orthogonal basis see "basis orthogonal"
Orthogonal complement 190 257
Orthogonal decomposition see "decomposition orthogonal"
Orthogonal expansion see "expansion orthogonal"
Orthogonal function theory 155
Orthogonal measure see "measure orthogonal"
Orthogonal multiresolution see "multiresolution orthogonal"
Orthogonal projection see "projection orthogonal"
Orthogonal sum 210 257
Orthogonal wavelet see "wavelet orthogonal"
Orthogonality 17 129 197
Orthogonality relations 13 57
Orthogonality, filter 87
Orthogonality, wavelet xxxii—xxxiv 5
Orthonormal basis see "basis orthonormal"
p-Bernoulli product measure see "measure p-Bernoulli
p-subinterval 166
P.A.M. Dirac 58 234 235
Parseval basis see "basis Parseval"
Parseval frame see "frame Parseval"
Parseval identity 13 32 66 99 103 104 137 162 168 191 193 210 228
Parseval system 13
Parseval wavelet see "wavelet Parseval"
Partial isometry see "isometry partial"
Partition 166
Partition, non-overlapping 165 186
Path 7 87 123 124 127 129
Path space see "space path"
Perfect, reconstruction 87 124 132 205
Periodic, function see "function periodic"
Permutation of bases see "basis permutation
Permutative representation see "representation permutative"
Perron xliii
Perron — Frobenius — Ruelle theory 99 see Perron Perron Perron Perron Perron
Phase modulation 198
Phase transition 33 34 87
Physics xxviii xxxi xxxiii xxxv 33 154 see
Physics mathematical 6
Pixel 33
Plancherel formula 164
Pointwise convergence see "convergence pointwise"
Poisson integral 50
Poisson measure see "measure Poisson"
Polar decomposition 150 201
Positional number system xx 33 40 69
Powers-Stormer 138 154
probability xxviii—xxxi xxxiii xliv 6 17 18 33—37 84 87 88 108 125 168
Probability conditional 45 254
Probability distribution, Gaussian see "distribution Gaussian"
Probability measure see "measure probability"
Probability space see "space probability"
Probability, free 177
Probability, non-commutative 37 177
Probability, transition see "transition probability"
Process xxviii xxx 48 49 86
Process, branching 5 see
Process, Markov see "Markov process"
Process, operator-valued see "operator process"
Processing see "signal processing"; "image processing"
PRODUCT 76 114 115 207 see
Product measure see "measure product"
Product, cartesian 43 257
Product, Cauchy see "Cauchy product"
Product, infinite see "infinite product"
Product, inner 9 75 114 193 212 257
Product, matrix see "matrix product"
Product, operator see "operator product"
Product, random 34 84
Product, Riesz see "Riesz product"
Product, tensor xxvii 6 56 58 109 142 147—149 151 152 158 165 168 179 180 186 189 257 see tensor"
Projection 10 55 94 112 117 173 216 228
Projection, final 173
Projection, initial 173
Projection, orthogonal 10 135 141 167 216
Projection-valued measure see "measure
Pure 169
Pyramid 125 127 158 159 173 188 226
Pyramid algorithm see "algorithm pyramid"
Pyramid, dyadic 159
Pyramid, singly generated 159
Quadrature xxix 131 227 228
Quadrature mirror see "filter quadrature-mirror"
Quantization xxxi 224—226
Quantum field theory xxix 154
Quantum particle 15
Quantum physics xxix xxxii 37
Quantum statistical mechanics see "statistical mechanics quantum"
Quantum theory 131
| Quantum-mechanical state see "state quantum-mechanical"
Quarter Cantor set see "Cantor set quarter"
Quarter division 21
Quasi—free state see "state quasi—free"
R- xxxiv 43 50 79 91
R-harmonic function see "harmonic function
R-invariant see "invariant
R. Gundy xxxiii xliii 6 33 87
R. Strichartz 26 76 80 87
Radon measure see "measure Radon"
Radon — Nikodym derivative see "derivative Radon
Random 18 59 83
Random model, viii 2 8 9 12 21 26 40 41 83 98 136
Random on branches xxviii xxx 70
Random on fractal 21
Random process 36 55 204
Random product see "product random"
Random variable xviii 55—57
Random walk vi xviii xxiv xxviii—xxx xxxiv xliii 4—7 16 21 34 39 40 42 48 57 77 83 84 87 100 see
Random,  - xxiv
Random, Gaussian 56 57
Range subspace 117 162
Reconstruction see "perfect reconstruction"
RECURSIVE 129 131
Recursive algorithm see "algorithm recursive"
Recursive system 197
Redundancy 228 229
refinement 4
Refinement, equation 111
Regularity xxxiv 5 80 87 107
Regularity, Dini 4
Regularity, Lipschitz 4
Renormalization group see "group renormalization"
Renormalize xxix
Representation xxix 124 140 165 172 190 197 214 254—256
Representation of  by translation 111
Representation of algebraic structure xxix 37
Representation of CAR algebra 138
Representation of Cuntz algebra 5 22 131 136 139 152 154 155 158 161—164 167 168 170 174 179 180 182 183 187 192 196 205 211 214 218 219 227
Representation theory 154 155 180
Representation, base-point 219
Representation, boundary see "boundary representation"
Representation, irreducible 183
Representation, matrix 140 218
Representation, N-adic 90 101 256
Representation, permutative 6 180 184 185 189 190 194
Representation, spectral 112
Representation, subband 219
Representation, unitary equivalence of 184
Representation, wavelet 102 182
Reproduction formula 144
Resolution xix xxii xxvi xxix xxx 9 10 22 33 111 147 148 181 225 230 see
Resolution subspace xxvi 23 109 110 123 126 152 180 207 255
Resolution, multiply generated 114
Resolution, visual xvi xviii xx xxii 40 225
Riesz product 84 97
Riesz's theorem see "theorem Riesz's"
Row-contraction 217 222
Ruelle see also "eigenfunction Perron Perron Perron Perron Perron
Ruelle measure see "measure Ruelle"
Ruelle operator see "operator H"
Ruelle's theorem see "theorem Ruelle's"
S. Mallat, xxxii 33 168
Sampling 17 18 21 36 37 213 215
Sampling theory 5 18
Sampling, down- 87 124 128 132 133 205 206 212 213 257
Sampling, Shannon xxxi 18
Sampling, up- 87 124 132 205 206 212 213 257
Scale number 19 40 70 147 190 see
Scale-N, wavelet see "wavelet scale-N"
Scaling xxii xxiii 3 22 23 25 69 80 99 100 110 111 123 142 181 186 188 195 198 208
Scaling dimension see "dimension scaling"
Scaling equation, wavelet 25
Scaling function xx xxx 3 4 12—14 16 23 25 64 111 134 207 256
Scaling identity xx 3 10 14 15 17 25 30 91 102 103 109 111 123 130 131 134 199 209
Scaling in the large 14
Scaling number 143 146 147 188 208
Scaling operator see "operator scaling"
Scaling relation 3 75
Scaling transformation 9 66 79 80
Scaling, Cantor 14
Scaling, Daubechies XXXV 12 13 125
Scaling, dyadic 2 3 110 162 181 192 200 208 209 255
Scaling, fixed 3 9 10 22 66 188
Scaling, Haar, xxxv 13 14 103
Scaling, stretched Haar 12 13 103
Scaling-similarity 9 33 180
Schmidt's decomposition theorem see "theorem Schmidt's"
Segment 165 166 186 257
Self-similarity xxix xxxv 9 48
Separation of variables 158 179
Shannon sampling see "sampling Shannon"
Shift-invariant see "invariant shifter-"
Signal analysis xvi xxvi 40 223
Signal processing vi—viii xv xvi xix—xxii xxvi xxviii xxxi—xxxvii xliv 4 6 10 18 23 25 26 33 37 39 87 123—125 130 131 135 155 181 187 189 205 206 210—212 215 216 218 219 223 224 227—229 231 see
Singly generated xxx 159 160 173
Six-tap 22 146
slanted see "matrix slanted"
Space, compact Hausdorff 101
Space, detail 33 123 255
Space, Euclidean 22
Space, Euclidean, ambient 81
Space, function xxii xxvi 9 22 59 109 130 142 146 147 157 158 179 190 207 210 228 251
Space, function, ambient 3
Space, Hilbert xviii—xxi xxiii xxvii xxxvi 3 5 6 10 14 15 22 28—31 33 36 37 58 71 79 87 93 97 109 110 114 136 139 140 142—144 147—152 157 158 161 162 165 169 170 172 174 176 180—184 186 188 189 196—199 204 207 210 212 213 217 218 221 222 228—230 251 252 254 257
Space, Hilbert geometry xxvi 109 142 148 179 198 207 221 230
Space, Hilbert, ambient 25 26 142 152 188 207 229
Space, Hilbert, complex 58 114 143 144 173 182—184 203 252
Space, Hilbert, dilated 229 230
Space, Hilbert, fractal 14 17 72 97 110 158 196 198
Space, Hilbert, operators in xxxii 6 37 131 138 142 143 161 177 180 183 209—211 216 218 221 251
Space, Hilbert, symbolic 110
Space, path xxix 5 6 34 see path-space"
Space, probability xviii xxiv 5 7 9 21 22 37 47 50 55 56 60 70 114 135 203 233 255 256
Sparse matrix see "matrix sparse"
Spectral analysis 158 181
Spectral measure see "measure spectral"
Spectral pair 36 71 74
Spectral representation see "representation spectral"
Spectral theorem see "theorem spectral"
Spectral theory xliv 37 57
Spectral transform 110
Spectrum 34 138 254
Spectrum, peripheral 57
Speech signal xxxi 124 205 227
State xviii xxiii 6 26 37 139—141 151 154 157 256
State on graph configuration 35
State, equilibrium 154
State, multi- 139
State, quantum-mechanical xviii xxxii 154
State, quasi—equivalent 154
State, quasi—free 138 139 154
Statistical mechanics 33 34 42 87 154
Statistical mechanics, quantum 34 154
Statistics xxxi xxxiii 154
Stone — "Weirstra theorem see "theorem Stone
Stone — Weierstra theorem see "theorem Stone
Stretched Haar wavelet see "wavelet Haar stretched"
Subband 23 124 205 215 227
Subband Coding xxxi 123
Subband filter see "filter subband"
Subband representation see "representation subband"
Subband, frequency see "frequency subband"
Subdivision xxxii xxxv 4 123 124 195
Subdivision algorithm see "algorithm subdivision"
Subdivision, dyadic xxxv
Subdivision, Mallat see "Mallat subdivision"
Subinterval 167
Subinterval N-adic see "N-adic subinterval"
Subinterval p- see "p-subinterval"
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