Lectures on harmonic analysis / Thomas H. Wolff ; edited by Izabella Laba and Carol Shubin.

Format:

Book

Author/Creator:

Wolff, Thomas H.

Contributor:

Łaba, Izabella, 1966-

Shubin, Carol, 1958-

Series:

University lecture series (Providence, R.I.) ; 29.

University lecture series, 1047-3998 ; v. 29

Language:

English

Subjects (All):

Harmonic analysis.

Fourier analysis.

Physical Description:

x, 137 pages : illustrations ; 26 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society, 2003.

Contents:

Chapter 1. The L[superscript 1] Fourier Transform 1

Chapter 2. The Schwartz Space 7

Appendix Pointwise Poincare inequalities 11

Chapter 3. Fourier Inversion and the Plancherel Theorem 15

Corollaries of the inversion theorem 18

Chapter 4. Some Specifics, and L[superscript p] for p [less than sign] 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

Chapter 11. Recent Work Connected with the Kakeya Problem 91

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.

Notes:

Includes bibliographical references (page 137).

ISBN:

0821834495

OCLC:

52559253