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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
Subinterval, dyadic fractional      see "dyadic fractional subinterval"
Subspace, invariant      see "invariant subspace"
Subspace, resolution      see "resolution subspace"
Substitution, iterated      34
Symbolic dynamics      see "dynamics symbolic"
Synthesis      124 132 205 206 227 see
Tap number      147 see
Tensor      140 148 150 162
Tensor factorization      see "factorization tensor"
Tensor product      see "product tensor"
Theorem, "Fatou's lemma"      101
Theorem, "Kolmogorov's lemma"      48 149
Theorem, "Schwarz's inequality"      31
Theorem, "Zorn's lemma"      172
Theorem, dominated convergence      65 79
Theorem, Fatou - Primalov      48 50
Theorem, Fubini's      191
Theorem, Karhunen - Lo'{e}ve      55 58 148 204
Theorem, Kolmogorov's      204
Theorem, martingale convergence      21 48 51 92
Theorem, Perron — Frobenius      34 see
Theorem, Riesz's      37 45 46 141
Theorem, Ruelle's      xxxiv see
Theorem, Schmidt's      58 148 150
Theorem, Spectral      39 55 58 110 112 150 201
Theorem, Stone — Weierstra$B$      27 39 43—46 79
Theorem, Szego's limit      154
Theorem, uniqueness      86
Tiling      87 124 165 166 182 185—189
Tiling, dyadic      187
Tiling, self-affine      100
Time-localized function      see "function time-localized"
Torus      25 204 251 see
Trace formula      34
Trace, normalized      184
Traditional wavelet setup      xxx 4 6 10 25 26 71 110 112
Transfer operator      see "operator transfer"
Transformation group      see "group transformation"
Transformation rule      165 166 see
Transition measure      see "measure transition"
Transition operator      see "operator transition"
Transition probability      xxxiv 5 9 12 17 19 21 34 37 39—41 48 50 59 62 63 70 254
Translation      110 111 198
Translation, integer      126 see
Translation-invariant      see "invariant translation-"
TREE      xxxiv 5 42 87 124 see
Two-cycle      160
Two-tap      146
Tychonoff infinite-product topology      7 43
Uniqueness theorem      see "theorem uniqueness"
Unit interval      62 90 137 139 166
Unitarity      132 174 175 183 191 220
Unitary      xix
Unitary equivalence      151 163 169 184
Unitary extension principle      107 222
Unitary isomorphism      see "isomorphism unitary"
Unitary matrix      see "matrix unitary"
Unitary operator      see "operator unitary"
Unitary scaling operator      see "operator scaling unitary"
Unitary, infinite-dimensional — group      see "group infinite-dimensional
Up-sampling      see "sampling up-"
Variable, dual      see "dual variable"
Variable, Fourier-dual      see "Fourier dual"
Variable, random      see "random variable"
W. Heisenberg      58 131 176 179 235 236
W. Lawton      xxxiii xliii xliv 21 33 57 87
Walk      6 41 128 see
Wavelet      vi vii xv-xvii xix xx xxv-xxx xxxii—xxxvi xliii xliv 1—7 9 14 16 17 22 23 25 33—37 39 40 57 58 64 71 79—81 83 87 91 99 100 104 105 107 109 111 122 130 131 142 151 152 155 158 179 182 189 190 211 222—230 235 256 see
Wavelet algorithm      see "algorithm wavelet"
Wavelet analysis      xv xx xxviii xxx xxxii xxxiii xliii 4 6 10 34 57 60 84 98 99 109 181 188 208 210 225 226
Wavelet basis      see "basis wavelet"
Wavelet coefficient      see "coefficient wavelet"
Wavelet construction      xix xxix—xxxi xxxiii 1 4 5 7—9 13 14 36 57 83 97 119 121—124 130 131 136 157 179 180 192 198
Wavelet decomposition      see "decomposition wavelet"
Wavelet expansion      230
Wavelet filter      xxxii xxxiii 5 23 33 37 83 87 112 122 130 136 227 230
Wavelet matrix      see "matrix wavelet"
Wavelet orthogonality      see "orthogonality wavelet"
Wavelet packet      vi xxxiv xxxv 4 6 22 35 110 117 122—126 129—131 136 142 153 159 176 180 187—189 256
Wavelet packet, algorithm      see "algorithm wavelet
Wavelet packet, dyadic      127 158 159
Wavelet representation      see "representation wavelet"
Wavelet scale-N      64 65 190 252
Wavelet theory      xxix 9 33 87 110 168 177 222—224
Wavelet transfer operator      see "operator transfer wavelet"
Wavelet transform      142 186
Wavelet transform, discrete      142 180 202
Wavelet transition operator      see "operator transition wavelet"
Wavelet, band-limited      4
Wavelet, compactly supported      xxx 14
Wavelet, Daubechies      5 14 121 122 124 127 128 134—136 228
Wavelet, dual      xxxii
Wavelet, dyadic      15 39 99 123—125 146
Wavelet, fractal      15 71 180
Wavelet, frame      see "frame wavelet"
Wavelet, frequency-localized      xxx 7
Wavelet, frequency-localized function      vi xvi xx xxvii xxx 1 16 102 103 123 134 256
Wavelet, frequency-localized, Daubechies      110
Wavelet, frequency-localized, Haar      103
Wavelet, gap-filling      22 72
Wavelet, Haar      xvi xxxi 5 12—14 99 102 103 106 119 124 127 128 131 148 192 229
Wavelet, Haar, dyadic      136 137
Wavelet, Haar, stretched      12 13 15 16 99 100 104 106 252
Wavelet, matrix-valued      22
Wavelet, multiresolution      xxx 10 16 97 110 142 181 190
Wavelet, multi—      see "multiwavelet"
Wavelet, N-adic      64 123
Wavelet, orthogonal      124
Wavelet, Parseval      13 16 103 105
Wavelet, time-frequency      xxxi
Wavelet, time-scale      xxxi
Wavelet, traditional — setup      see "traditional wavelet setup"
Wavepacket coefficient      see "coefficient wavepacket"
Weight function      see "function \mathcal{W}-"
Wold decomposition      see "decomposition Wold"
Y. Meyer      xxxii 33 176
Zeta function      see "function zeta"
Zorn's lemma      see "theorem "Zorn's
1 2 3 4
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