Overview

Discussing many results and studies from the literature, this work illustrates the value of Fourier series methods in solving difficult nonlinear PDEs.

Methods and Applications

Using these methods, the author presents results for stationary Navier-Stokes equations, nonlinear reaction-diffusion systems, and quasilinear elliptic PDEs and resonance theory.

Connections and Extensions

He also establishes the connection between multiple Fourier series and number theory, presents the periodic Ca-theory of Calderon and Zygmund, and explores the extension of Fatou's famous work on antiderivatives and nontangential limits to higher dimensions.

Significance

The importance of surface spherical harmonic functions is emphasized throughout.