algorithm, method, 219
analysis, Gabor, 186
analysis, multiresolution, 26, 381
analysis, multiresolution,
anisotropic, 249
analysis, time-frequency, 186
anisotropy, 237
atom, 12
atom, anisotropic, 245, 375
atom, boundary, 215
atom, 350
atom, (s,p)*, 352
atom, (s,p)*-£, 352
atom, 350, 369
atom, (s,p)k,l, 12
atom, (s,p)%L, 245
atom, 15
atom, 130
atom, (s,p)cr, 63
atom, (s,p)a, 16, 131
ball means, 72, 74, 387
basis, Haar, 29
basis, Schauder, 28
basis, unconditional, 29
Besicovitch, 78
characterisations by differences, 72
characteristics, Besov, 93, 101, 121,
260, 314, 323
characteristics, Bessel, 339
characteristics, Courant, 93
characteristics, multifractal, 93, 101,
314, 323
class, Muckenhoupt, 273
condition, ball, 146
condition, porosity, 146
cone, positive, 84
convergence, local, 153
convergence, unconditional, 14, 34,
153, 270
convergence, absolute, 133, 17
Courant, R., 87
curve, Koch, 359
curve, snowflake, 359
d-set, 91, 96, 313, 315, 357
(d, 4r)-set, 97
d-space, 113, 358, 363
d-space, regular, 358, 373
decomposition, Whitney, 208, 209
Deutsche Mark, Zehn, 125
differences, iterated, 198
differences, symmetric, 319
dimension, Fourier, 303
dimension, Hausdorff, 121
distance, anisotropic, 241
distribution, radial, 288
distribution, tempered, 3, 4, 127
domain in Rn, 58, 194
domain, interior regular, 393
domain, Lipschitz, 64, 195
embedding, compact, non-compact,
197 (proof) embedding, constants, 231
embedding, limiting, 284
embedding, sharp, 58, 77, 40, 43, 258
embedding, weighted, 266, 279
envelopes, 77, 39
envelope, continuity, 50
envelope, growth, 48, 52
Euclidean chart, 119, 358, 363
£-chart, 358, 363, 369
£-frame, 364
F in F*q, 170
formula, Stirling, 168
Fourier transform, 4, 129
frame, 24, 169
frame, dual, 169, 174
frame representation, 350
function, admissible, 53
function, Courant, 92
function, Gauss, 186
function, Lipschitz, 195
function, strictly increasing, 95, 307
function, scaling, 26
T-function, 168
Gaufi, C.F., 125
Gausslet, 125, 186
Gausslet, (s,p)-/3, 187
^-philosophy, 124
guy, bad, 122
guy, good, 125
h-set, 96
i7-frame, 365
frame, 365
homogeneity property, 132
index-shifting, 19
index set, main, 209
index set, residual, 210
inequality, Carl, 58
inequality, maximal, 384, 393
information map, 219
interpolation, 69, 272
interpolation, entropy, 57
isomorphic, 157
A;-wavelet, 147, 154, 268
king, of function spaces, 122
Koch, 359
Laplacian, Dirichlet, 86
lattice, approximate, 21, 109
local means, 9, 247
localisation principle, 269
localisation, refined, 207
fjL-property, 81, 83, 298
mass distribution, 316
maximal function, 5, 384
mean smoothness, 238
measure, diffuse, 96
measure, doubling, 96
measure, Hausdorff, 121
measure, isotropic, 95, 307
measure, lacunary, 316
measure, Radon, 80
measure, strongly diffuse, 96
measure, strongly isotropic, 96, 307
measure, tame, 315
measure, Weyl, 99, 344
method, transference, 256, 286
modulus of continuity, 387
molecules, 171
Muckenhoupt class, 273
multiplication algebra, 136
multipliers, pointwise, 136
Nash, J., 79
non-smooth, 78
not dense, 145
Nullstellenfreiheit, 87
number, approximation, 56, 68, 228
number, entropy, 56, 61, 228, 258, 372
number, sampling, 219
operator, compact, 56
operator, extension, 65, 108, 349
operator, identification, 88, 103,
304, 342
operator, restriction, 64
operator, trace, 82, 104, 106, 303
operator, universal extension, 66
p-norm, 55
para-basis, 203, 214
porous, 146, 393
positivity, 190, 390
potential, Bessel, 190, 301
potential, Riesz, 301, 372
property, Fat ou, 273
property, Fubini, 290
property, Weyl, 98
quark, (s,p)K-f3, 21, 22
quark, (s,p)-/3, 110, 347
quark, (s,p)-Z, 365
quasi-metric, 112, 357
quasi-norm, 55
rearrangement, 42, 44
reproducing formula, 377
resolution of unity, 4, 129, 21, 110
sampling method, 219
scaling property, 205
set, residual, 332
sheep, black of calculus, 122
smoothness, dominating mixed, 25
smoothness, generalised, 25, 53, 55
smoothness, pointwise, 184
smoothness, variable, 53, 55
smoothness, varying, 184
snowflaked version, 114
space, anisotropic, 374
space, Besov, classical, 4
space, Besov, classical anisotropic, 235
space, Besov, anisotropic, 256
space, Besov, homogeneous, 273
space, Besov, weighted, 268
space, dual, 88, 150, 248
space, Hardy, 4, 217, 240
space, Hardy, anisotropic, 240
space, Holder-Zygmund, 3, 15, 76
space, Holder-Zygmund, anisotropic, 243
space, of homogeneous type, 113
space, Lipschitz, 364
space, Lorentz, 156
space, modulation, 187
space, quasi-metric, 112, 357
space, radial, 287
space, resilient, 125
space, Schwartz, 4, 127
space, sequence, 273
space, Sobolev, 3, 76
space, Sobolev, anisotropic, 239
space, Sobolev, classical, 2
space, Sobolev, classical anisotropic, 235
space, Sobolev, fractional, 3
space, Sobolev, weighted, 267, 285
space, tailored, 108
space, two-microlocal, 185
space, weighted, 264
space, Zygmund, 156
support, singular, 121, 322
system, dual, 163
theorem, Paley-Littlewood, 2, 240, 268
theorem, representation, atomic, 63
theorem, representation, quarkonial, 22,111
theorem, representation, smooth
atomic, 13
theorem, representation, wavelet, 33, 154
theorem, representation, wavelet
frames 37, 39
transform, snowflaked, 119, 125, 359
transform, snowflaked, anisotropic, 362
ultra-distribution, 265
wavelet, 26, 147, 203
wavelet, basis, 27, 154
wavelet, Daubechies, 31, 204, 253
wavelet, father, 26
wavelet, Haar, 28
wavelet, in domains, 209, 214
wavelet, Meyer, 31, 160, 254
wavelet, mother, 26
wavelet, smooth 30
wavelet system, main, 210
wavelet system, residual, 210
weight, 263
Weyl, H., 86
window, 186
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