edited by R Coifman (Yale University)

Table of Contents (35k)
Introduction (46k)
Chapter 1.1: Overview and general discussion (197k)
Chapter 1.2: Fourier integral operators (158k)
Chapter 1.3: Related questions from geometric measure theory (178k)

This book contains five theses in analysis, by A C Gilbert, N Saito, W Schlag, T Tao and C M Thiele. It covers a broad spectrum of modern harmonic analysis, from Littlewood–Paley theory (wavelets) to subtle interactions of geometry and Fourier oscillations. The common theme of the theses involves intricate local Fourier (or multiscale) decompositions of functions and operators to account for cumulative properties involving size or structure.

• L^p → L^q Estimates for the Circular Maximal Function (W Schlag)
• Three Regularity Results in Harmonic Analysis (T Tao)
• Time-Frequency Analysis in the Discrete Phase Plane (C M Thiele)
• Multiresolution Homogenization Schemes for Differential Equations and Applications (A C Gilbert)
• Local Feature Extraction and Its Applications Using a Library of Bases (N Saito)