Fourier Integrals in Classical Analysis
Fourier Integrals in Classical Analysis
Fourier Integrals in Classical Analysis is an advanced monograph concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. Using microlocal analysis, the author, in particular, studies problems involving maximal functions and Riesz means using the so-called half-wave operator. This self-contained book starts with a rapid review of important topics in Fourier analysis. The author then presents the necessary tools from microlocal analysis, and goes on to give a proof of the sharp Weyl formula which he then modifies to give sharp estimates for the size of eigenfunctions on compact manifolds. Finally, at the end, the tools that have been developed are used to study the regularity properties of Fourier integral operators, culminating in the proof of local smoothing estimates and their applications to singular maximal theorems in two and more dimensions.
Product details
No date availablePaperback
9780521060974
252 pages
228 × 151 × 15 mm
0.384kg
Table of Contents
- Background
- 1. Stationary phase
- 2. Non-homogeneous oscillatory integral operators
- 3. Pseudo-differential operators
- 4. The half-wave operator and functions of pseudo-differential operators
- 5. Lp estimates of eigenfunctions
- 6. Fourier integral operators
- 7. Local smoothing of Fourier integral operators
- Appendix. Lagrangian subspaces of T*IRn.
