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| Jorgensen P.E.T. — Analysis and Probability: Wavelets, Signals, Fractals |
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| Предметный указатель |
 -measurable see "measurable
-measure see "measure
 -normalization 12
 -sequence 140
 —normalization 12
 - 100
 -random variable see "random variable
 -additive see "measure
-algebra xviii xxiv 27 28 37 40 47 94 149 204 251—253 255
-algebra, Borel xxiv 43 251
-algebra, sub- xxiv 37
-algebra, tail- 37
-algebras, countable family of 37
-invariant see "invariant
2-fold branch mapping see "branch mapping  -fold"
A. Cohen xxxii xxxiii 33 87
A. Grossman xxxii
A. Haar xvi xxvi xxxi 131 223
a.e. convergence see "convergence a.e."
A.N. Kolmogorov xxvi xxxi 7 8 39 43 46 59 84 168 170 203 204 235
Abelian see "algebra abelian"; abelian";
Absolutely continuous see "measure absolutely
Adjoint see "matrix adjoint"; adjoint"
Affine fractal xxiii 3 5 15 22 26 70—72 77 80 180 194 198
Affine iterated function system 5 14 15 25 67 70—72 80 81
Affine iteration 21
Affine map xxiii 1 3 5 81 195
Affine self-tiling see "tiling self-affine"
Affine wavelet frame see "frame affine
Algebra xvii xx 1 3 27 43 44 47 54 140 176 251 252
Algebra - see "-algebra"
Algebra *- 221
Algebra fermion see "fermion algebra"
Algebra, abelian 110 138 139
Algebra, C*- see "C* -algebra"
Algebra, CAR- see "CAR-algebra"
Algebra, Cuntz see "Cuntz algebra"
Algebra, Cuntz - Krieger see "Cuntz-Krieger algebra"
Algebra, dense sub- 46
Algebra, matrix 139 210
Algebra, maximal abelian sub- see "maximal abelian subalgebra"
Algebra, non-abelian xxviii 138 139 155 218
Algebra, operator see "operator algebra"
Algebra, sub- 44 139 154 155
Algebraic structures, representations of "see representation of algebraic structure"
Algorithm xvi xix xx xxv xxvi xxxiii xxxiv xxxvi xliii 3 4 10 33 35 124 125 128 147 148 164 206 210 211 215 223—226 230 231
Algorithm, cascade see "cascade"
Algorithm, Euclid's xx 11 40 63 69 85 92 164 166
Algorithm, Gram - Schmidt xv xxvi
Algorithm, matrix xxvi xxviii xxxii 142 147 157 226 230 see
Algorithm, N-adic 125 126
Algorithm, pyramid vi xx xxxiv xxxv xlv 33 111—113 122 123 125 128 129 134 148 157—159 182 225 227 see
Algorithm, recursive xxvii xxxii xxxiv xxxv xlv 6 109 147 157 226
Algorithm, subdivision xxix xxxi xxxii xxxv 124 142 227
Algorithm, wavelet xiii xvi xix xxvii—xxix xxxi—xxxiii 25 33 110 123 125 133 142 147 148 151 152 156 206 210 215 226 227 230
Algorithm, wavelet packet xxxiv xxxv 3 34 123 125 126
Algorithm, wavelet-like xxv
Alias 229 230
Ambient Euclidean space see "space Euclidean ambient"
Ambient function space see "space function ambient"
Ambient Hausdorfif measure see "measure Hausdorff ambient"
Ambient Hilbert space see "space Hilbert ambient"
Analysis (engineering) xvi xxii xxvi 124 132 148 205—207 214 227 see
Analysis (mathematics) xvii xxvii—xxxi xxxiii xliv 3 6 9 22 26 33—35 37 39 59 80 81 84 87 98 206 see
Analysis, data xxv
Analysis, Fourier see "Fourier analysis"
Analysis, fractal see "fractal analysis"
Analysis, harmonic see "harmonic analysis"
Analysis, multiresolution see "multiresolution analysis"
Analysis, numerical xxvii xxxii 229
Analysis, spectral see "spectral analysis"
Analysis, stochastic 35
Analysis, wavelet see "wavelet analysis"
Approximation xxvi 4 6 79 90 107 109 158 226
Approximation attractor 34 187
Approximation automorphism*- 211
Approximation theory xxix
Approximation, atomic see "measure atomic"
Approximation, cascade see "cascade approximation"
Band-limited wavelet see "wavelet band-limited"
Base-point representation see "representation base-point"
Bases see "basis"
Basis xv xvi xx xxvi xxxi xxxvi xliv 2 5 9 22 30 59 67 70 71 87 111 143 146 148 157 162 179 182 184 228 229
Basis function xv xxxvi 104 106 112 113 129 166
Basis transformation 166
Basis wavelet dyadic 99 202
Basis wavelet fractal 180
Basis wavelet-like 109
Basis, bi—orthogonal 143
Basis, canonical 143 160 202
Basis, dual 143 144
Basis, Fourier xvi 67 144 158 168 193 252 255
Basis, fractal 21 26 70—72 79
Basis, frame 28 29 143 229
Basis, localized 67 80 157 158 see
Basis, orthogonal xxvi 36 69 70 87
Basis, orthonormal xxxi 13 15 16 22 26 28 29 32 36 55 56 65 71 72 74 76 77 79 99 103—106 130 139 140 143 144 149 150 162 163 165 166 168 177 182 184 185 189 190 192—194 197 198 228 229 254 255
Basis, Parseval 103
Basis, permutation of 182
Basis, recursive 179
Basis, wavelet xvi xix xxvi xxxiii xliii xliv 13 15 22 23 67 72 80 87 99 103 142 176 179 180 187—189 208 229 see
Bernoulli product measure see "measure p-Bernoulli—product"
Bethe lattice see "lattice Bethe"
Bi—orthogonal see "basis bi—orthogonal"
Black Box xx xxi
Borel -algebra see "-algebra Borel"
Borel cross section 183
Borel measure see "measure Borel"
Borel subsets 135 167 199
Boundary for harmonic function see "harmonic function boundary
Boundary Representation 19 48
Boundary value 21 43 48
Branch mapping 256
Branch mapping 2—fold 186 187
Branch mapping measurable 41
Branch mapping n-fold 184 185 188 189
Branching 5 158 161 see
Branching system 159 171
Branching, dyadic—system 160
Brownian motion xxvi xxvii 56 57
Brownian motion, fractal xxiii
Brownian motion, fractional xxvii 57
Brownian motion, s-fractal xxiii
C*-algebra xxix 5 6 131 138—140 142 151 154 155 183 211 251
C. Brislawn xxxiii xliv 22 234
C.E. Shannon xxxi 18
C.T. Ionescu Tulcea 57
Canonical anticommutation relations 5 138—140 154 251 see
Canonical basis vector see "basis canonical"
Cantor 1 69 179
Cantor constmction 69 70 74
Cantor group see "group Cantor"
Cantor measure see "measure Cantor"
Cantor scaling identity see "scaling identity Cantor"
Cantor set 2 5 15 71—73 252 255
Cantor's example see "measure Cantor"
Cantor, conjugate 73 75—77
Cantor, middle-third 2 5 14 15 21 25 27 69—71 73 74 80 176 189 195 251
Cantor, quarter 5 26 72—77 79 198
Cantor, scale 4 see quarter"
CAR-algebra 5 138 139 154 155
CAR-algebra, representations of see "representation of CAR-algebra"
Cascade 9 130 see nested
Cascade approximant 134
Cascade approximation 4
Cauchy product 87 206
Closed linear span 15 169 200 207 209 252
Closed subspaces, nested family of xviii—xx xxii xxix 9 33
Co-isometry 162 216
Cocycle 43 48—52 91 92 255
| Cocycle identity 19 20
Cocycle property 49
Coefficient 168
Coefficient, autocorrelation 104
Coefficient, filter 4
Coefficient, Fourier xvi xxii 87 97
Coefficient, masking 4 10 16 23 87 91 114 123 130 131 135 227
Coefficient, matrix 131
Coefficient, operator 114
Coefficient, response 10
Coefficient, wavelet xxvi 23 25 202 225 227 230
Coefficient, wavepacket 168
Combinatorial probability theory 5 154
Combinatorial tree 6 111 129
Commute 94 135 234 235 see
Compact 1 8 14 25 27 35 43 69 71 83 92 98 149 195 204
Compact abelian group see "group abelian compact"
Compact Hausdorff space see "space compact
Compact operator see "operator compact"
Compact support see "wavelet compactly
Composition of operators 210 216
Conditional expectation 10 57
Conjugate Cantor set see "Cantor set conjugate"
Conjugation 150
Consistency, xx 80 122 see
Continued fractions 41
Convergence xxviii xxx 4 6 9 10 18 80
Convergence of infinite product 5 8 11 17—19 21 60 85
Convergence, a.e. 32 50 56 92 95 96
Convergence, dominated 78 89
Convergence, dominated-theorem see "theorem dominated
Convergence, martingale-theorem see "theorem martingale
Convergence, pointwise 4 5 17—19
Countable family of -algebras see "-algebras countable
Cuntz algebra xxix 5 6 22 131 136 152 154 155 158 161 162 179—183 187 196 205 208 210 222 254 255 see
Cuntz relations xxii 6 132 155 160 161 174 179—182 201 203 211 214 216 219 221 222 227 231 254 see
Cuntz representation see "representation of Cuntz algebra"
Cuntz system 208 221
Cuntz — Krieger algebra xxix
CYCLE 26 87
Cyclic group see "group cyclic"
Cylinder set 43 47 78 85 115 139 251
D. Donoho xxxiii
D. Dutkay xliii 57 72 87 97 194
D. Gabor xxxi
D. Hilbert xxxi 205
D. Ruelle xliii 33 34 87 155
Data Mining xvii xix xxiv xxv xxviii 107 224
Daubechies scaling function see "scaling function Daubechies"
Daubechies wavelet see "wavelet Daubechies"
Daubechies, decision tree xxxv
Decomposition 166
Decomposition, Karhunen - Lo'{e}ve see "theorem Karhunen
Decomposition, orthogonal 172
Decomposition, Schmidt's see "theorem Schmidt's"
Decomposition, wavelet xxxii 190
Decomposition, Wold 169
Derivative, Radon — Nikodym 50 53
Detail space see "space detail"
Differentiability 6
Differentiable xxxii—xxxiv 14 135
DIMENSION 4 33 117 154 210
Dimension, fractal 14 195 251
Dimension, Hausdorff xxiii 2 71 72 74 77 176 195 251 254
Dimension, scaling 72
Dini regularity see "regularity Dini"
Dirac mass 26 102 255
Dirac notation 55 58 182 186 257
Discrete wavelet transform see "wavelet transform discrete"
distribution xxiii 130 142 168 204
Distribution, Gaussian 56 203 see Gaussian"
Down-sampling see "sampling down-dual"
Down-sampling basis see "basis dual"
Down-sampling filter see "filter dual"
Down-sampling high-pass filter see "filter dual
Down-sampling lattice see "lattice dual"
Down-sampling low-pass filter see "filter dual
Down-sampling variable xxi 206 212
Down-sampling wavelet see "wavelet dual"
Down-sampling, Fourier" see "Fourier dual"
Duality 69 205 207 212
Duality for Cantor sets see "Cantor set duality
Duality for Cantors 69
Duality, Fourier 35 60 81 207 209 210
Duality, particle-wave 131
Duality, time-frequency 207 212
Dyadic branching system see "branching dyadic
Dyadic fractional subinterval 166—168
Dyadic Haar wavelet see "wavelet Haar dyadic"
Dyadic pyramid see "pyramid dyadic"
Dyadic rationals 66 90 167
Dyadic representation 166
Dyadic scaling see "scaling dyadic"
Dyadic subdivision see "subdivision dyadic"
Dyadic tiles see "tiling dyadic"
Dyadic wavelet see "wavelet dyadic"
Dyadic wavelet packet see "wavelet packet dyadic"
Dynamics xxix xxx xxxvi xliv 9 34 37 42 168
Dynamics, complex 25 34
Dynamics, symbolic xxxv 34 182
Eigenfunction 19
Eigenfunction, minimal 15 19 99—102 105 252
Eigenfunction, Perron — Frobenius 26 97 252
Eigenspace 19
Eigenspace, Perron — Frobenius 107
Eigenvalue 9 11 19 77 100 107 116
Endomorphism xxxiv 4 52 91 101 184 256
Engineering xiii xxviii xxxi xxxii xxxiv-xxxvi xliv 17 87 88 124 204 210 212 215 227 228 230
Equivalence class 172 183
Equivalence relation 172
Ergodic theory xliv 84
Ergodicity 155
Euclid's Algorithm see "algorithm Euclid's"
Euclidean algorithm see "algorithm Euclid's"
Exchange of limits 89 101
expansion xxxi 168
Expansion, Fourier see "Fourier expansion"
Expansion, N-adic 11
Expansion, orthogonal xxix
Expansion, wavelet 23 25
Extension, unitary matrix 107
Extension, unitary — principle see "unitary extension principle"
Factorization 34
Factorization of unitary operators 158 180
Factorization, matrix 210
Factorization, operator 216
Factorization, Schmidt's see "theorem Schmidt's 168 170 181 186 190 194 198
Farey tree 41 42
Father function see "function father"
Fatou - Primalov theorem see "theorem Fatou-Primalov"
Fatou set 25
Fatou's lemma see "theorem "Fatou's
Fermion 139 154
Fermion algebra 154
Filter xxxiii 4 87 124 133 205 206 210 213 215 227 231 253
Filter orthogonality see "orthogonality filter"
Filter, dual 124 205
Filter, dual high-pass 124 132
Filter, dual low-pass 124 132
Filter, high-pass 23 87 111 124 125 132 154 205 253
Filter, low-pass xxxiv 4 23 37 87 104 111 124 125 132 154 204 205 253
Filter, quadrature-mirror 3 4 10 23 40 87 135 168 186 205 212 217 227 228
Filter, subband xxix xxxiv 23 26 87 123 124 126 205 210 211 213 215 228
Filter, wavelet see "wavelet filter"
Fixed-point problem 10
Four-tap vi 22 134 135 146 147 202 228
Fourier analysis xv xxviii 2 30 225 226
Fourier basis see "basis Fourier"
Fourier coefficient see "coefficient Fourier"
Fourier correspondence 67
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