Wave packet analysis / Christoph Thiele
Material type: TextSeries: Regional Conference Series in MathematicsPublication details: Rhode Island American Mathematical Society 2006Description: 86 pISBN:- 9780821836613
- 515.2433 THI-C
Item type | Current library | Collection | Shelving location | Call number | Status | Notes | Date due | Barcode | Item holds |
---|---|---|---|---|---|---|---|---|---|
Books | BITS Pilani Hyderabad | 510 | General Stack (For lending) | 515.2433 THI-C (Browse shelf(Opens below)) | Checked out | DST Project Book: Dr. Manish Kumar | 14/07/2024 | 38342 |
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515.2433 RUZ-M Fourier analysis : pseudo-differential operators, time-frequency analysis and partial differential equations / | 515.2433 SIM-B Harmonic analysis : | 515.2433 SOM-K Insight into wavelets : from theory to practice / | 515.2433 THI-C Wave packet analysis / | 515.2433 VRE-A Fourier analysis and its applications / | 515.2433 WAL-D Introduction to wavelet analysis / | 515.2433 WAL-D Introduction to wavelet analysis / |
The 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.
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