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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
$B$-measurable      see "measurable
$B$-measure      
see "measure
$L^{1}$-normalization      
12
$l^{2}$-sequence      140
$L^{2}$—normalization      12
$P_{x}$-      100
$\mathcal{A}$-random variable      see "random variable
$\sigma$-additive      see "measure
$\sigma$-algebra      
xviii xxiv 27 28 37 40 47 94 149 204 251—253 255
$\sigma$-algebra, Borel      xxiv 43 251
$\sigma$-algebra, sub-      xxiv 37
$\sigma$-algebra, tail-      37
$\sigma$-algebras, countable family of      37
$\sigma$-invariant      see "invariant
2-fold branch mapping      
see "branch mapping $2$-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 $\sigma$-      see "$\sigma$-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 $\sigma$-algebra      see "$\sigma$-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 $\sigma$-algebras      see "$\sigma$-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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