000			nam a22 7a 4500
999			_c39093 _d39093
008			190302b2006 xxu||||| |||| 00| 0 eng d
020			_a9780821836613
082			_a515.2433 THI-C
100			_aThiele, Christoph
245			_aWave packet analysis / _cChristoph Thiele
260			_aRhode Island _bAmerican Mathematical Society _c2006
300			_a86 p.
365			_aUSD _b32.00.
440			_aRegional Conference Series in Mathematics.
500			_aThe concept of ``wave packet analysis'' originates in Carleson's famous proof of almost everywhere convergence of Fourier series of $L2$ 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. Carleson's original theorem is sometimes cited as one of the most important developments of 20th century harmonic analysis. The set of ideas stemming from his proof is now seen as an essential element in modern harmonic analysis. Indeed, Thiele won the Salem prize jointly with Michael Lacey for work in this area. 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.
650			_aWalsh functions
650			_aWave packets
650			_aWavelets (Mathematics)
650			_aLinear operators