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Jorgensen P.E.T. — Analysis and Probability: Wavelets, Signals, Fractals
Jorgensen P.E.T. — Analysis and Probability: Wavelets, Signals, Fractals



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Название: Analysis and Probability: Wavelets, Signals, Fractals

Автор: Jorgensen P.E.T.

Аннотация:

This book, combining analysis and tools from mathematical probability, focuses on a systematic and novel presentation of recent trends in pure and applied mathematics: the emergence of three fields, wavelets, signals and fractals. The unity of basis constructions and their expansions is emphasized as the starting point for the development of bases that are computationally efficient for use in several areas from wavelets to fractals.

The book brings together tools from engineering and math, especially from signal- and image processing, and from harmonic analysis and operator theory. The presentation is aimed at graduate students, as well as users from a diverse spectrum of applications.


Язык: en

Рубрика: Технология/

Статус предметного указателя: Готов указатель без номеров страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 332

Добавлена в каталог: 14.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $\mathcal{A}$-      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 $\mathbb{Z}$ 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$B$ theorem      see "theorem Stone
Stone — Weierstra$B$ 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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