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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
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, $L^{2}$-      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, $\sigma$-      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, $\mathcal{B}$-      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, $\sigma$-finite      31 253
Measure theory      viii 5 6 20 22 70 195 204
Measure, $\mathcal{B}$      53
Measure, $\sigma$-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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