Bøger af Yves Meyer

Image compression, the Navier-Stokes 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 "e;oscillating patterns"e;, which are present in many natural images, help to explain nonlinear equations, and are pivotal in studying chirps and frequency-modulated 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 JPEG-2000. The second chapter has new results on the Navier-Stokes and other nonlinear evolution equations. Frequency-modulated 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 Besov-type function spaces and leads to many deep results, including new generalizations of famous Gagliardo-Nirenberg and Poincare inequalities. This book is based on the "e;Dean Jacqueline B. Lewis Memorial Lectures"e; 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 frequency-modulated signals. Most of the material in the book did not appear previously in monograph literature.

Now in paperback, this remains one of the classic expositions of the theory of wavelets from two of the subject's leading experts. An essential purchase for anyone carrying out research on wavelets and their applications.

This long-awaited updated edition includes completely new chapters on four topics: wavelets and the study of turbulence, wavelets and fractals (which includes an analysis of Riemann's nondifferentiable function), data compression, and wavelets in astronomy.

Constantin presents the Euler equations of ideal incompressible fluids and the blow-up problem for the Navier-Stokes equations of viscous fluids, describing major mathematical questions of turbulence theory.