Wave packet analysis

"The concept of "wave packet analysis" originates in Carleson's famous proof of almost everywhere convergence of Fourier series of L[superscript 2] functions. It was later used by Lacey and Thiele to prove bounds on the bilinear Hilbert transform. For quite some time, Carleson's wave packet analysis was thought to be an important idea, but that it had limited applications. But in recent years, it has become clear that this is an important tool for a number of other applications. This book is an introduction to these tools. It emphasizes the classical successes (Carleson's theorem and the Hilbert transform) in the main development. However, the book closes with a dedicated chapter on more recent results." "The book gives a nice survey of important material such as an overview of the theory of singular integrals and wave packet analysis itself. There is a separate chapter on "further developments", which gives a broader view on the subject, though it does not exhaust all ongoing developments."--BOOK JACKET.