University Lecture Series 2001; 122 pp; softcover Volume: 22 ISBN10: 0821829203 ISBN13: 9780821829202 List Price: US$30 Member Price: US$24 Order Code: ULECT/22
 Image compression, the NavierStokes equations, and detection of gravitational waves are three seemingly unrelated scientific problems that, remarkably, can be studied from one perspective. The notion that unifies the three problems is that of "oscillating patterns", which are present in many natural images, help to explain nonlinear equations, and are pivotal in studying chirps and frequencymodulated signals. The first chapter of this book considers image processing, more precisely algorithms of image compression and denoising. This research is motivated in particular by the new standard for compression of still images known as JPEG2000. The second chapter has new results on the NavierStokes and other nonlinear evolution equations. Frequencymodulated signals and their use in the detection of gravitational waves are covered in the final chapter. In the book, the author describes both what the oscillating patterns are and the mathematics necessary for their analysis. It turns out that this mathematics involves new properties of various Besovtype function spaces and leads to many deep results, including new generalizations of famous GagliardoNirenberg and Poincaré inequalities. This book is based on the "Dean Jacqueline B. Lewis Memorial Lectures" given by the author at Rutgers University. It can be used either as a textbook in studying applications of wavelets to image processing or as a supplementary resource for studying nonlinear evolution equations or frequencymodulated signals. Most of the material in the book did not appear previously in monograph literature. Readership Graduate students and researchers working in functional analysis and its applications, in particular to signal and image processing. Table of Contents  Still images compression
 The role of oscillations in some nonlinear PDE's
 Frequency modulated signals, chirps and the Virgo program
 Conclusion
 References
