Wave Packet Analysis

The concept of wave packet analysis originates in Carleson's famousproof of almost everywhere convergence of Fourier series of $L2$functions. It was later used by Lacey and Thiele to prove bounds onthe bilinear Hilbert transform. For quite some time, Carleson's wavepacket analysis was thought to be an important idea, but that it hadlimited applications. But in recent years, it has become clear that thisis an important tool for a number of other applications. This book is anintroduction to these tools. It emphasizes the classical successes(Carleson's theorem and the Hilbert transform) in the maindevelopment. However, the book closes with a dedicated chapter onmore recent results. Carleson's original theorem is sometimes cited asone of the most important developments of 20th century harmonicanalysis.