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| Авторизация |
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| Поиск по указателям |
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| Pinsky M.A. — Introduction to Fourier Analysis and Wavelets |
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| Предметный указатель |
Abel means 45 64 261 266
Abel sums 49
Abelian theorem 54
Abel’s lemma 167
Absolutely continuous functions 21
Absolutely convergent trigonometric series 3 43
Almost-everywhere convergence 20 28 49 153 346
Analytic function 22 172
Approximate identitites 45 97
Averaging 118
Banach space 75
Banuelos, R 202
Beckner, W. 174 175
Benedicks, M.r 240
Bernoulli, D. 1
Bernstein’s inequality 122
Bernstein’s Theorem 43 70 129 350
Berry — Essen theorem 276
Bessel functions 6 81 140 154 164
Bessel’s inequality 36
Boas, R. P. 228
Bochner — Riesz summability 152
Bochner, S. 139
Bochner’s method of subordination 106
Bochner’s theorem on positive-definite functions 220 270
Borel — Cantelli Lemmas 281
Bounded linear operator 75
Bounded variation 27 60
Brando'ini, L. 149
Brownian motion 299
Calderon — Zygmund decomposition 209
Calderon — Zygmund theorem 211
Calderon, A. P. 194 196 209
Cantor measure 20
Cantor — Lebesgue theorem 87
Cantor’s uniqueness theorem 86
Carleson, L. 73 118
Central limit theorem 260
Cesaro average 119
Cohen’s theorem 338 262
Colzani, L. 149
Compactly supported wavelets 326
Completeness of the Haar functions 295
Completeness of the Hermite functions 138
Conjugate function 176
Conjugate Poisson kernel 8 179
Continuity theorem 269
Continuum wavelet 286
Contraction operator 14
Convergence of wavelet expansions 341
Convex function 170
Convex sequence 96
Convolution 5 14 19 92
Convolution semigroups 272
Daubechies’ formula 331
De la Vallee Poussin means 68
de — Moivre Laplace theorem 100
Dilation matrix 354
Dini condition 27 89
Dini’s theorem 115
Dirac measure 20
Directed set 46
Dirichlet kernel 15 25 1 12 140 223
Dirichlet — Jordan theorem 27 117
Dirichlet, P. G. 27
Distribution function 181
Divergence of Fourier series 73
du Bois — Reymond 73 1 17
Dyadic projections 292
Equidistribution mod 1 57
Euler formula 4
Exponential function 6
Factorial function 6
Fatou’s theorem 50 214
Fefferman, C. 73
Fejer means 45 54 62 98 120
Fejer — Riesz lemma 330
Finite measures 19 119 256 273
Fourier coefficient 4 13 19
Fourier cosine transform 124
Fourier reciprocity formula 4 14 93 97 231
Fourier sine transform 125
Fourier transforms 89 102 256 323
Fourier, J. B. 2
Gap series 262
Gauss — Weierstrass kernel 97
Gaussian approximation 80
Gaussian density function 95 257
Gaussian summability 104 232
Gaussian wavelet 288
Generalized h-transform 125
Gibbs — Wilbraham phenomenon 31 115
Grunbaum, A. 133
Haar function 387 306
Haar series 291 296
Haar wavelet 291 321
Hardy — Littlewood maximal function 197
Hardy, G. H. 59
Hardy’s Tauberian theorem 59
Harmonic functions 212
Hausdorff — Young inequality 174
Heat flow 2
Heat kernel 97 203 223
Hemandez — Weiss formula 333
Herglotz theorem 215
Hermite polynomials 134
Higher-order approximation in  66
Hilbert transform on  184 224
Hilbert transform on  176 224
Hoelder means 53
Hoelder’s inequality 170
Holder condition 13 40 63 116
Homogeneous Banach space 47 98
Hormander condition 211
Hunt, R. 73 118
Huygens’ principle 148
Independent random variables 261
Infinitely differentiable function 21
Integration of Fourier series 29
Isoperimetric inequality 38
Jackson’s theorem 65 348
Jordan, C. 27
Kac 266
Kahane, J. P. 45 73 143
| Katznelson, I. 73 180
Kendall’s Theorem 241
Kolmogorov, A. N. 73 118 179
Kolmogorov’s inequality 192
Landau’s asymptotic formula 243
Laplace asymptotic method 6 9 80
Laplace’s equation 9 106 212
Large scale analysis 345
Lattice points 241
Laurent series 5
Law of the iterated logarithm 280
Lebesgue constants 61 75
Lebesgue Differentiation Theorem 200
Lebesgue set 124
Levy modulus of continuity 302
Levy — Khintchine Theorem 273
Lipschitz continuity 62
Lusin, N. 73
Marcinkiewicz interpolation theorem 206
Marcinkiewicz, J. 169 179
Maxwell’s theorem 109 259
Mexican hat wavelet 288
Meyer wavelets 318
Modified Bessel function 6 81 85
Modulus of continuity 12 20
Moore, C. 202
Multi-resolution analysis 303
Multiple Fourier series 230 244
Multiple harmonic motion 1
Negative binomial series 52
Newtonian potential kernel 109
Non-tangential convergence 202
Null-integrability 325
One-sided Fourier representation 124
Orthogonality 2 137
Orthonormal wavelet 319
Parseval’s identity 35
Periodic function 13
Periodization 223
Piecewise smooth function 21 145
Pinsky 139 145 147
Plancherel’s theorem 128
Pointwise convergence criteria 25 115 139 233 298 347
Poisson kernel 7 15 46 90 106 189
Poisson summation formula on 238
Poisson summation formula on R 1 225
Positive-definite function 257
Quotient groups 355
Radial functions 92 157 202 245
Random walk 252
Rapidly decreasing function 96
Rates of convergence in 61
Rates of convergence in  39
Restriction theorem 158
Riemann localization 31
Riemann means 64
Riemann — Lebesgue lemma 18 94
Riesz 73
Riesz kernels 195
Riesz potential kernel 107
Riesz systems 304 356
Riesz — Fischer theorem 37
Riesz — Thorin interpolation theorem 169
Rotations 194
Salem, R. 266
Scaling equation 310 357
Scaling filter 312
Scaling functions 304 319
Schrodinger equation and Gauss sums 247
Schwartz class 96
Schwartz distribution 146
Self-adjoint operator 15
Shannon sampling theorem 228
Shannon scaling function 306
simple harmonic motion 1
Simultaneous non-localization 240
Sine integral 24 114 185
Singular integrals 183 194 210
Skew-adjoint operator 16 176
Smith, К. T 202
Smoothness of wavelets 334
Sobolev Norm 43 290
Spherical Fourier inversion 139
Spherical maximal function 203
Spherical mean value 140
Spherical partial sum 139 233
Stationary phase method 162
Stein, E. 157 159 175 202 204 211
Stein’s complex interpolation method 159 175
Stirling’s formula 6
Strichartz, R. 33
Stronger summability method 52
Structure constants 310 357
Subgroups 354
Sublinear operator 197 207
Summability matrix 51
Summation by parts 11 79
Symmetric partial sum 4 112
Systems of wavelets 352
Tail sum 12
Tauberian theorem 54
Taylor, M. E 139 147 248
Tempered distribution 108 129
Three-lines theorem 172
Tomas, P. 159
Translation error 40
Uncertainty principle 134
Uniform boundedness principle 76 84
Uniform continuity 98
Uniform convergence 4
Uniqueness of Fourier coefficients 17
Upper half plane 216
Vibrating string 1
Wave equation 171
Wavelet transform 285
Wavelets 284
Weak convergence of measures 268 327
Weierstrass Af-test 4
Weiss, G 157
Whittaker, E. T 228
Wiener covering lemma 198
Wiener’s theorem 57 110
Young’s inequality for convolutions 174
Zygmund, A. 20 44 72 209 236 262 266
Zygmund’s theorem 44 209
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