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