Meyer Y. — Wavelets and Operators :: Электронная библиотека попечительского совета мехмата МГУ

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Meyer Y. — Wavelets and Operators

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Название: Wavelets and Operators

Автор: Meyer Y.

Аннотация:

The mathematical theory of wavelets has proved to be a powerful tool for harmonic analysts, and an alternative to the standard theory of Fourier analysis. The aim of this first textbook is to describe the foundations of so-called wavelet analysis, emphasizing its roots in mathematics.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 223

Добавлена в каталог: 26.11.2005

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Предметный указатель

$2\pi$ -periodic      2
$B^{s,q}_{p}$       see "Inhomogeneous Besov space"
$H^{1}(\mathbb{R}^{n})$ (Stein — Weiss space)      138 140 141 192
$H^{p}(\mathbb{R}^{n})$       176
$H^{s}(\mathbb{R}^{n})$       43
$W^{s,p}$       44
$\dot{C}^{\gamma}$       175
$\dot{L}^{p,s}$       173
$\mathbb{H}^2(\mathbb{R})$       135 197 202
$\mathcal{D}'(\mathbb{R})$       2
$\mathcal{D}(\mathbb{R})$       2
$\mathcal{S}_{r}(\mathbb{R}^{n})$       40
Aliasing      11
Amplifier design      14
Amplitude modulation      54
Ascoli's theorem      52
atom      142
Atomic $H^{1}$       142
Atomic decomposition      14
Atomic representation      190
Atomic sequence      145
Base of an atom      145
Belongs      144
Bergmann space      197
Bernstein's inequalities      14 30 32 46
Besov space      50 186 198 199
Besov space, inhomogeneous      50 51
Beurling algebra      186 192
Bloch space      197
BMO space      69
Borel's method      7
Brownian motion      6 128
Calderon — Zygmund operator      xiii 165 203
Calderon's identity      125 126 196
Cancellation      95 108 see
Carleson's condition      123 141 154 162
Carleson's theorem      9
Coherent states      16
Communication theory      18
Complex Hardy space $\mathbb{H}^2(\mathbb{R})$       158
Constructive field theory      71 127
Convergent Series      118
Converges commutatively      139
Converges conditionally      138
Converges unconditionally      138 161
Convolution product      5
Cutoff      129
Daubechies' condition      132
Daubechies' theorem      96
David — Journe theorem      164
Dirac comb      2
Dirac measure      9
Disc algebra A(D)      70
Discrete Hilbert transform      13
Dyadic $H^{1}$ space      156
Dyadic blocks      6
Dyadic interpolation      63
Extension operator      57
Father wavelet      67 72 200
Filtering      9
Filtering operators      76
Finite elements      57
Fourier coefficients of a function      2
Fourier integral      7
Fourier inversion      8
Fourier series      112
Fourier transform      9
Frame      131
Franklin system      70
Freud's construction      119
Full wavelet series      113 122
Function with centre $x_{0}$ , width d, type s      178
Groechenig's algorithm      83
Growth at infinity      110
Haar system      73 82 109 207
Hadamard-lacunary Fourier series      123
Hardy space $\mathbb{H}^{p}$       14
Hausdorff — Young inequality      14

Heisenberg's uncertainty principle      19 20
Hilbert transform      4 159
Hoelder function of exponent s      118
Hoelder spaces      178
Hoermander class $S^{0}_{\rho,\delta}$       54
Holomorphic wavelet      202
Hump algebra      189 192
Image processing      62
Innovation space      60 82
Iteration      127
John — Nirenberg space      140 151 157
Khinchin's inequality      141 165
Lacunary Fourier scries      113 120
Lacunary wavelet series      113 122
Lagrangian spline      24
Lebesgue point      34
Littlewood — Paley theorem      6 20
Littlewood — Paley wavelet      125
localization      66 67 108
Lusin's area function      14 159 160
Magnification      145
Mallat's construction      97
Marcinkiewicz's Theorem      166
Maurey's theorem      156
Maximal characterization      158
Maximum principle      44
Molecular decomposition      150
Molecule      151
Morlet wavelets      130
Morlet's iterative algorithm      130
Mother wavelet      66 71
Multi-dimensional wavelets      83 107
Multipliers      140
Multiresolution approximation      20 21 38 41 50
Multiresolution approximation of Litlewood — Paley type      25 60 65 75 120
Multiresolution operators      57 62
One-dimensional wavelets      71 96
Orthogonal projection      45
Oscillation condition      66 67
p-atom      176
p-molecule      178
Paley — Wiener algebra      9
Plancherel's identity      3 133
Poisson summation formula      4
Pseudo-differential operators      54
Quantum field theory      173
Random Fourier series      123
Regularity      29 66 67 108
Renormalization      71 125 127—129 183
Reproducing kernel      48
Restriction operator      57 see
Riesz basis      21 25 136
Sampling      9 30
Sampling operator      22
Saw-tooth function      4
Schauder basis      115
Schauder basis of a Banach space      139
Schwartz space $\mathcal{S}(\mathbb{R})$       8
Shannon's condition      10 20 76
Sobolev embedding      186
Socle of a sequence      144
Sparse series      113 122
Special atoms      193
Spline Function      59 74
Stroemberg's construction      70 124
Summable family      139
Support of a sequence      144
Takagi's fractal function      120
Tent space      15 144
Two-dimensional wavelets      81 87
Unconditional basis      117 161 163
Unconditional Schauder basis      139
Very special atoms      193
Wavelet coefficient      17
Wavelet of class m      66
Wavelet series      112
Wavelet with two humps      202 206
Wiener algebra $A(\mathbb{R})$       7 116 186
Zygmund class $\Gamma_{*}$       52 121 180 181

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