By Yves Meyer

Picture compression, the Navier-Stokes equations, and detection of gravitational waves are 3 likely unrelated medical difficulties that, remarkably, should be studied from one standpoint. The inspiration that unifies the 3 difficulties is that of "oscillating patterns", that are found in many usual photos, aid to give an explanation for nonlinear equations, and are pivotal in learning chirps and frequency-modulated signs. the 1st bankruptcy of this ebook considers snapshot processing, extra accurately algorithms of photo compression and denoising. This examine is encouraged particularly by means of the recent normal for compression of nonetheless photos often called JPEG-2000. the second one bankruptcy has new effects at the Navier-Stokes and different nonlinear evolution equations. Frequency-modulated indications and their use within the detection of gravitational waves are coated within the ultimate bankruptcy. within the ebook, the writer describes either what the oscillating styles are and the maths invaluable for his or her research. It seems that this arithmetic consists of new homes of varied Besov-type functionality areas and results in many deep effects, together with new generalizations of well-known Gagliardo-Nirenberg and Poincaré inequalities. This booklet is predicated at the "Dean Jacqueline B. Lewis Memorial Lectures" given by way of the writer at Rutgers collage. it may be used both as a textbook in learning purposes of wavelets to picture processing or as a supplementary source for learning nonlinear evolution equations or frequency-modulated indications. many of the fabric within the booklet didn't look formerly in monograph literature

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