Frames and Harmonic Analysis

Cover......Page 1
Title page......Page 4
Contents......Page 6
Preface......Page 8
Participants of the AMS Special Session “Frames, Wavelets and Gabor Systems”......Page 10
Participants of the AMS Special Session “Frames, Harmonic Analysis, and Operator Theory”......Page 12
1. Introduction......Page 14
2. Preliminaries......Page 15
3. A continuum of BTFs in ℝ³......Page 16
4. Harmonic BTFs......Page 19
5. Steiner BTFs......Page 21
6. Plücker ETFs......Page 26
References......Page 30
1. Introduction......Page 34
2. Preliminaries......Page 35
3. Phase retrieval by hyperplanes......Page 36
4. An example in \RR⁴......Page 41
References......Page 43
1. Introduction......Page 46
2. Real Vandermonde-like matrices......Page 47
3. Frames seeded from DFT matrices......Page 54
References......Page 57
1. Introduction......Page 60
2. General tools and models......Page 63
3. An extension of traditional compressed sensing......Page 66
4. Application to dense spectrum estimation......Page 70
5. Conclusion......Page 72
References......Page 73
1. Introduction......Page 76
2. From Kadison-Singer problem to Weaver’s conjecture......Page 77
3. Proof of Weaver’s conjecture......Page 85
4. Applications of Weaver’s conjecture......Page 96
Acknowledgments......Page 102
References......Page 103
1. Introduction......Page 106
2. Banach modules and memory decay......Page 107
3. The method of similar operators and a special case of the main result......Page 112
4. Proof of the main result......Page 115
5. Various classes of operators with memory decay......Page 116
6. Examples......Page 123
References......Page 125
1. Introduction......Page 128
2. Connection with projection methods and row action methods......Page 130
3. Convergence rate of Kaczmarz algorithm under noise......Page 134
4. Connection with statistical learning methods......Page 136
References......Page 138
1. Introduction......Page 142
2. Scattering network......Page 143
3. Filter aggregation......Page 150
4. Examples of estimating the Lipschitz constant......Page 156
References......Page 163
1. Introduction......Page 166
2. Translation operator on graphs......Page 169
3. Support of Laplacian Fiedler vectors on graphs......Page 175
References......Page 186
1. Introduction......Page 188
2. Weighted convolution inequalities and Beurling densities of the measure ⁻¹......Page 192
3. Best constants in weighted convolution inequalities......Page 197
4. Exponential weights......Page 211
References......Page 212
1. Introduction......Page 214
2. Preliminaries......Page 217
3. Problem 1 (=2)......Page 219
4. Problem 2......Page 220
5. Remarks and open problems......Page 224
References......Page 225
1. Introduction......Page 228
2. One prime power......Page 231
3. Szabó’s examples......Page 236
4. Some general constructions......Page 240
5. Appendix......Page 244
References......Page 246
1. Introduction: Hutchinson measures and determining when they are spectral......Page 248
2. Spectral Hutchinson-3 measures: a necessary condition on  for the resulting measure to be spectral......Page 253
3. Well-spacedness about the origin and the canonical spectrum......Page 255
4. Well-spacedness about the origin and an alternative spectrum......Page 263
5. Which Hutchinson-3 measures are spectral?......Page 264
Acknowledgements......Page 266
References......Page 267
1. Introduction......Page 268
2. Lebesgue measure: kernels in ²() with equal norms......Page 272
3. Diagonal coefficient matrices......Page 274
4. Absolutely continuous measures......Page 278
5. Preservation of norms of subspaces of ²()......Page 279
References......Page 282
1. Introduction......Page 284
2. Daubechies and Coiflets tight framelets for two generators......Page 286
3. The Gibbs phenomenon in Daubechies and Coiflets tight framelet expansions......Page 289
References......Page 294
1. Introduction......Page 296
2. Conditions for shape preservaton......Page 297
References......Page 303
-Markov measures, transfer operators, wavelets and multiresolutions......Page 306
1. Introduction......Page 307
2. General theory......Page 308
3. Solenoid probability spaces......Page 327
4. Examples and applications: Transfer operators and Markov moves......Page 339
References......Page 352
Back Cover......Page 358