Wavelets Through a Looking Glass: The World of the Spectrum (Applied and Numerical Harmonic Analysis) Hardcover – Import, 12 July 2002

This book is easy to read, straight to the point, uses easy vocabulary and a pleasant style. As the book's subtitle says "The world of the spectrum" it actually delivers what it says: the world of the spectrum for wavelets!. The looking glass the authors are referring to is Fourier transforms, as such the book take a beautiful well written easy to read journey into the wavelets world with all about spectrum analysis right from the very beginning with a looking glass through Fourier transforms. To me, the book has been a jewel and a rarity to hold in your hands; such a master piece. It helps a lot if you are familiar with spectrum analysis, eigenvalues, eigenvectors, and FFT and what Fourier transform is. But to my great delight the book also makes these topics seem approachable and quite in reach, the authors do not dive into unnecessary detail or diverge at all, and have managed to stay the course on what they want to offer and remain focused: wavelets, wavelets and more wavelets understanding in areas, views and perspectives that might not have been presented often times elsewhere. Bottom line, two very enthusiastic thumbs up for this book indeed.

Spectral theory forms a natural environment for the study of wavelets. The use operator algebras is unique and interesting. The text is written such that the analysis is precise and clear throughout. The book reads nicely without being chatty or overly terse and tiresome. Many of tge proofs are extremely well laid out. The problems are carefully chosen (ranging from challenging to knock your socks off bruisers!) so get your erasers out. Mathematicians, computer scientists, theoretical physicists working in quantum computing will likely find this book useful. Recommended to anyone working with wavelets. A little bit of functional analysis will come in handy for those of wanting to do a self study.

This is an important mathematical reference written in excellent style. Wavelets have found applications in many areas of engineering and CS. The authors provide a detailed, rich and entertaining tour through this relatively young but important field for both math and CS/Eng. Connections are, e.g., made between advanced CS virtual-reality applications such as audio-systems processing, future applications such as quantum computing, and advanced math in functional analysis and operator theory.