Editorial Boar d Jerry L . Bon a (Chair ) Nige l J . Hitchi n Jean-Luc Brylinsk i Nicola i Reshetikhi n 2000 Mathematics Subject Classification. Primar y 35Q30 , 42C40 , 65T60 , 76D05 , 76D06 . ABSTRACT. Thi s boo k i s aime d a t bridgin g a ga p betwee n signa l processing , imag e processing , and nonlinea r differentia l equations . Mor e precisel y th e rol e playe d b y oscillatin g pattern s wil l be emphasized . Thes e pattern s occu r a s th e texture d component s o f images . The y als o occu r i n frequency modulate d signal s o r chirps . Wha t i s mor e surprisin g i s th e relevanc e o f suc h pattern s in partia l differentia l equations . The firs t hal f o f thi s essa y ca n b e use d a s a textbook , sinc e full y detaile d proof s ar e given . Library o f Congres s Cataloging-in-Publicatio n Dat a Meyer, Yves . Oscillating pattern s i n imag e processing an d nonlinea r evolutio n equation s : th e fifteenth Dea n Jacqueline B . Lewi s memoria l lecture s / Yve s Meyer . p. cm . (Universit y lectur e series , ISS N 1047-399 8 v. 22 ) Includes bibliographica l references . ISBN 0-8218-2920- 3 (alk . paper ) 1. Evolutio n equations , Nonlinear . 2 . Image compression . 3 . Signal processing—Mathematics . 4. Oscillations . I . Universit y lectur e serie s (Providence , R.I. ) 22. QA377.M495 200 1 515'.353—dc21 2001041268 Copying an d reprinting . Individua l reader s o f thi s publication , an d nonprofi t librarie s acting fo r them , ar e permitte d t o mak e fai r us e o f th e material , suc h a s t o cop y a chapte r fo r us e in teachin g o r research . Permissio n i s grante d t o quot e brie f passage s fro m thi s publicatio n i n reviews, provide d th e customar y acknowledgmen t o f th e sourc e i s given . Republication, systemati c copying , o r multipl e reproductio n o f any materia l i n this publicatio n is permitte d onl y unde r licens e fro m th e America n Mathematica l Society . Request s fo r suc h permission shoul d b e addresse d t o the Assistan t t o the Publisher , America n Mathematica l Society , P. O . Bo x 6248 , Providence , Rhod e Islan d 02940-6248 . Request s ca n als o b e mad e b y e-mai l t o reprint-permission@ams.org. © 200 1 b y th e America n Mathematica l Society . Al l right s reserved . The America n Mathematica l Societ y retain s al l right s except thos e grante d t o th e Unite d State s Government . Printed i n th e Unite d State s o f America . @ Th e pape r use d i n thi s boo k i s acid-fre e an d fall s withi n th e guideline s established t o ensur e permanenc e an d durability . Visit th e AM S hom e pag e a t URL : http://www.ams.org / 10 9 8 7 6 5 4 3 2 1 0 6 0 5 0 4 0 3 0 2 0 1
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