Akram Aldroubi

Review of Wavelets through a Looking Glass: The World of the Spectrum by Ola Bratteli and Palle Jorgensen, Applied and Numerical Harmonic Analysis, Birkhäuser, Boston, 2002.

The Book by Bratteli and Jorgensen is a superb book on wavelet's theory. It is very well written and has new and a fresh point of view on the subject. Although there are several good books on wavelets, the book by Bratteli and Jorgensen covers an important niche that has not been covered before. In particular

• 1- The book covers the theory of wavelets from the point of view of operators and functional analysis and will appeal to a growing number of pure as well as applied mathematicians interested in the subject.
• 2- The writing of the book is very appealing: every chapter starts by a tutorial that gives motivation as well as intuition. It is then followed by a very clean mathematical development of the subject, together with many examples, figures, and applications from physics and engineering. A set of nice problems is provided at the end of each chapter. Thus this book can be used as a graduate textbook or for mathematical seminars in mathematics departments.
• 3- This book can even be used by experts in wavelet theory for learning about recent developments and new perspectives from operator theory and functional analysis.