By Ola Bratteli

ISBN-10: 0817642803

ISBN-13: 9780817642808

ISBN-10: 0817681442

ISBN-13: 9780817681449

ISBN-10: 1461264154

ISBN-13: 9781461264156

ISBN-10: 3764342803

ISBN-13: 9783764342807

"Mere phrases can't effectively describe all of the nice positive aspects of the book...which has whatever for everybody of all mathematical persuasions.... This booklet has particularly a unique viewpoint from the opposite monographs on wavelets...mainly since it emphasizes the Fourier area because the right "window" or "looking glass" from which you could most simply research wavelet theory.... no matter what his or her point of workmanship with the topic, a reader of this publication is not really bored.... each one bankruptcy starts off with an introductory part obtainable to the layperson, frequently containing a few ancient heritage, and infrequently tremendous entertaining.... this can be a enjoyable booklet, packed with intriguing new effects, written via world-renowned specialists within the box, which makes connections among quite a few vital components in natural and utilized mathematics."

**—SIAM Review**

"This is a relatively strange wavelet booklet, with a clean view at the topic. whereas nearly all of wavelet books pay attention to multiresolution research and its purposes, this ebook treats the subject from an operator theoretic perspective, with a spotlight on strategies having a geometrical or spectral theoretic style. in truth, whereas elements of the e-book can be utilized in a wavelet direction, different elements will be compatible in a path directed in the direction of operator theory."

**—Zentralblatt Math**

"The authors take a clean examine the topic and enhance a brand new instinct for plenty of issues. specifically, they make extra vast use of spectral idea than is common within the topic. every one [chapter has] an creation to the subjects within the bankruptcy and explains why they're mentioned and the place they arrive from. There are connections with many different components of arithmetic and physics now not frequently linked to wavelet thought . . . the tip of every bankruptcy has a wide choice of difficulties during which a lot of the normal thought might be labored out by way of the reader. there's additionally a thesaurus of important phrases on the finish of bankruptcy 1 the place a number of the phrases . . . are in actual fact outlined either from a mathematical and an functions element of view."

**—Mathematical Reviews**

"This booklet does a superlative task of demonstrating the richness of the speculation of wavelets . . . The authors have established extra connections with spectral thought, ergodic conception, homotopy thought and the idea of chance . . . even as the fabric is fantastically documented via . . . figures . . . and illustrations . . . The pedagogy is extra greater via a number of paragraphs of illuminating prose at first of every bankruptcy . . . even supposing now not written as a standard textual content, . . . an industrious graduate scholar may possibly revenue greatly from publicity to this booklet. With recognize to the literature on wavelets, it's tricky to bear in mind the other booklet that's so good documented either with graphical and numerical info in addition to mathematical facts. This quantity will stay a imperative paintings for a few years to come."

**—Mark Pinsky, Northwestern University**

"This ebook by means of Bratteli and Jorgensen serves as an creation to the idea of wavelets and in addition a citing thus far with the most recent study difficulties. whereas there are lots of strong books on wavelets, 'Wavelets via a having a look Glass' brings a clean viewpoint at the box. the idea is roofed from the perspective of operator concept and sensible research, with an emphasis at the connection among the spectral houses of the operators at the discrete info and the geometric gains of the wavelet services within the non-stop counterpart. The booklet contains the now classical result of wavelet conception, akin to the multiresolution development and the correlation to the move operator, in addition to a few new result of the authors (published right here for the 1st time), akin to the index theorem or a number of spectral preperties of the move operator." --- **J. Operator Theory**

"The e-book provides a basic persetnation of a few fresh advancements in wavelet idea, with an emphasis on innovations which are either basic and comparatively undying haveing a geometrical and spectral-theoretic flavour. The exposition is obviously influenced and unfolds systematically aided through a variety of pix. first-class photographs express how wavelets rely on the spectra of the move operators. a few new effects are offered for the 1st time." ---**EMS Newsletter**