Contents
Foreword vii
Preface ix
Chapter 1. The
L1
Fourier Transform 1
Chapter 2. The Schwartz Space 7
Appendix: Pointwise Poincar´ e inequalities 11
Chapter 3. Fourier Inversion and the Plancherel Theorem 15
Corollaries of the inversion theorem 18
Chapter 4. Some Specifics, and
Lp for p 2 23
Chapter 5. The Uncertainty Principle 31
Chapter 6. The Stationary Phase Method 37
Chapter 7. The Restriction Problem 45
Chapter 8. Hausdorff Measures 57
Chapter 9. Sets with Maximal Fourier Dimension and Distance Sets 67
Chapter 10. The Kakeya Problem 79
Bibliography 89
Chapter 11. Recent Work Connected with the Kakeya Problem 91
List of notation 93
11.1. The two dimensional case 93
11.2. The higher dimensional case 101
11.3. Circles 105
11.4. Oscillatory integrals and Kakeya 117
Bibliography 129
Historical Notes 133
Bibliography 137
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